1. If a quadrilateral's three angles are each 75 degrees, the fourth angle is (a) 150°(b) 135°(c) 45°(d) 75°
1. If a quadrilateral's three angles are each 75 degrees, the fourth angle is (a) 150°(b) 135°(c) 45°(d) 75°
Explanation:
(b) 135°
We are aware that the sum of a quadrilateral's internal angles is 360 degrees. It is clear from the question that a quadrilateral has three angles that are all equal to 75 degrees. Assume that x is the fourth angle.
Consequently, 75°+75°+75°+x=360°
225+x=360°
X=360°-225
x=135°
2. Which of the following diagonals cuts each other in half?
(a) Quadrilateral (b) kite (c) Trapezium (d) Square
2. Which of the following diagonals cuts each other in half?
(a) Quadrilateral (b) kite (c) Trapezium (d) Square
Explanation:
In a square
3. All angles are equal for which of the following figures?
A rectangle, a kite, a trapezium, a rhombus, and more
3. All angles are equal for which of the following figures?
A rectangle, a kite, a trapezium, a rhombus, and more
Explanation:
The rectangle (a)
Therefore, every angle in a rectangle is 90 degrees.
4. The diagonals of which of the following figures are perpendicular to one another?
(a) parallelogram (b) kite
(c) Trapezium (d) Rectangle
4. The diagonals of which of the following figures are perpendicular to one another?
(a) parallelogram (b) kite
(c) Trapezium (d) Rectangle
Explanation:
(b) Kite
Kite diagonals are parallel to one another, as depicted in the figure below.
5. Which of the following figures has equal diagonals?
Trapezium (optional) Rhombus
(c) Rectangle (d) Parallelogram
5. Which of the following figures has equal diagonals?
Trapezium (optional) Rhombus
(c) Rectangle (d) Parallelogram
Explanation:
Rectangle (d)
The following diagram demonstrates how equal diagonals apply to rectangles.
6. Which of the ensuing figures meets each of the conditions?
- There is agreement on all sides.
- There are no obtuse angles.
- The sides on either side are parallel
6. Which of the ensuing figures meets each of the conditions?
- There is agreement on all sides.
- There are no obtuse angles.
- The sides on either side are parallel
Explanation:
(c) R
Therefore, a square has all congruent sides, all right angles, and opposite sides that are parallel.
7. Which of the ensuing figures meets the criteria in question.
- Has two sets of neighbouring sides that are congruent.
7. Which of the ensuing figures meets the criteria in question.
- Has two sets of neighbouring sides that are congruent.
Explanation:
(C) R
8. Which of the ensuing figures fulfils the aforementioned property?
- Only one set of adjacent sides is parallel.
8. Which of the ensuing figures fulfils the aforementioned property?
- Only one set of adjacent sides is parallel.
Explanation:
(a) P
We can infer from the previous illustration that a trapezium only has one pair of parallel sides.
9. Which of the ensuing values does not meet any of the conditions?
- The odds are on the sides.
- There are no obtuse angles.
- The sides on either side are parallel.
9. Which of the ensuing values does not meet any of the conditions?
- The odds are on the sides.
- There are no obtuse angles.
- The sides on either side are parallel.
Explanation:
(a) P
10. We can conclude from the preceding figure that the trapezium does not meet any of the criteria listed in the question.
Which of the enumerated qualities best describes a trapezium?
(A) Two opposing sides are parallel.
(b) The diagonals cut each other in half.
(c) The diagonals are parallel to one another.
(d) Equal diagonals are present.
10. We can conclude from the preceding figure that the trapezium does not meet any of the criteria listed in the question.
Which of the enumerated qualities best describes a trapezium?
(A) Two opposing sides are parallel.
(b) The diagonals cut each other in half.
(c) The diagonals are parallel to one another.
(d) Equal diagonals are present.
Explanation:
(A) Parallel sides have opposite sides.
11. Which of the following describes a parallelogram's characteristics?
(A) The sides on either side are parallel.
(b) The diagonals form a right angle split across one another.
(c) The diagonals are parallel to one another in case
(d) Every angle is equal.
11. Which of the following describes a parallelogram's characteristics?
(A) The sides on either side are parallel.
(b) The diagonals form a right angle split across one another.
(c) The diagonals are parallel to one another in case
(d) Every angle is equal.
Explanation:
(A) The sides on either side are parallel.
12. Which number of obtuse angles can a quadrilateral have the most?
(a) 1 (b) 2 (c) 3 (d) 4
12. Which number of obtuse angles can a quadrilateral have the most?
(a) 1 (b) 2 (c) 3 (d) 4
Explanation:
(c) 3
Obtuse angle, as we know, is an angle between 90 and 180 degrees.
A quadrilateral's interior angles add up to 360 degrees. Therefore, none of the angles can be obtuse because the total would exceed 3600. There can only be three obtuse angles in a quadrilateral.
13. In an n-gon (a polygon with n sides), how many non-overlapping triangles may be created by connecting the vertices?
n -1 (a), n -2 (b), n -3 (c), n -4 (d), etc.
13. In an n-gon (a polygon with n sides), how many non-overlapping triangles may be created by connecting the vertices?
n -1 (a), n -2 (b), n -3 (c), n -4 (d), etc.
Explanation:
(b) n – 2
14. What does a pentagon's total number of angles equal?
a)180° b) 360° c) 540° d) 720°
14. What does a pentagon's total number of angles equal?
a)180° b) 360° c) 540° d) 720°
Explanation:
(c) 540°
A polygon's total angles are known to be (n - 2) 180 degrees. If the polygon's 'n' sides are how many,
Pentagon has 5 sides, hence n = 5 because of this.
So,(n-2)×180°
(5-2)×180°
3×180°
540°
15. How many angles are there in a hexagon?
A 180°, B 360°, C 540°, D 720°
15. How many angles are there in a hexagon?
A 180°, B 360°, C 540°, D 720°
Explanation:
(d) 720o
We are aware that (n - 2) 180o is the sum of all the angles in a polygon. where 'n' denotes the polygon's number of sides,
Hexagon therefore has 6 sides, so n = 6.
So, (n – 2) × 180°
(6-2)×180°
4×180°
720°
16. If the ratio of two adjacent angles in a parallelogram is (5x - 5)o and (10x + 35)o, then
(a) 1 : 3 (b) 2 : 3 (c) 1 : 4 (d) 1 : 2
16. If the ratio of two adjacent angles in a parallelogram is (5x - 5)o and (10x + 35)o, then
(a) 1 : 3 (b) 2 : 3 (c) 1 : 4 (d) 1 : 2
Explanation:
(a)1: 3
17. A __________ is a quadrilateral with all sides equal, equal opposite angles, and diagonals that bisect one another at right angles.
(a)Rhombus, (b) parallelogram, (c) square, and (d)Rectangle
17. A __________ is a quadrilateral with all sides equal, equal opposite angles, and diagonals that bisect one another at right angles.
(a)Rhombus, (b) parallelogram, (c) square, and (d)Rectangle
Explanation:
Rhombus (a)
A rhombus is a quadrilateral with all sides equal, equal opposite angles, and diagonals that cut each other at right angles.
18. An equal-angle quadrilateral is one with opposite sides and all angles.(a) square,(b) parallelogram, (c)rectangle, and (d)triangle (e) rhombus
18. An equal-angle quadrilateral is one with opposite sides and all angles.(a) square,(b) parallelogram, (c)rectangle, and (d)triangle (e) rhombus
Explanation:
rectangular (c)
19. A quadrilateral is considered to be equal-sided, diagonally, and at all angles. A square, a trapezium, a rectangle, a rhombus, and more
19. A quadrilateral is considered to be equal-sided, diagonally, and at all angles. A square, a trapezium, a rectangle, a rhombus, and more
Explanation:
In a square
20. How many diagonals are there in a hexagon?
(a) 9 (b) 8 (c) 2 (d) 6
20. How many diagonals are there in a hexagon?
(a) 9 (b) 8 (c) 2 (d) 6
Explanation:
(a)9
That much is obvious.
In a polygon with n sides, there are n(n-3)/2 diagonals.
Where n is 6
Then,
= 6 × (6 – 3)/2
= 6 × 3/2
= 18/2
= 9
21. A parallelogram is a shape whose adjacent sides are equal if and only if a rectangle, b a trapezium, c a rhombus, and d a square
21. A parallelogram is a shape whose adjacent sides are equal if and only if a rectangle, b a trapezium, c a rhombus, and d a square
Explanation:
Rhombus, c
22. A quadrilateral is a square if its diagonals are equal and bisect one another.
a rhombus, a rectangle, a square, a parallelogram, etc.
22. A quadrilateral is a square if its diagonals are equal and bisect one another.
a rhombus, a rectangle, a square, a parallelogram, etc.
Explanation:
Rectangle (b)
23. The total of a triangle's outer angles is equal to
180° (a), 360° (b), 540° (c), and 720° (d)
23. The total of a triangle's outer angles is equal to
180° (a), 360° (b), 540° (c), and 720° (d)
Explanation:
(b) 360°
360 degrees is the total of a triangle's outside angles.
24. Which of the following is an equiangular and equilateral polygon? (a)Square (b)Rectangle (c)Rhombus (d)Right triangle
24. Which of the following is an equiangular and equilateral polygon? (a)Square (b)Rectangle (c)Rhombus (d)Right triangle
Explanation:
(a)square
Square is an equiangular and equilateral polygon.
25. which one possesses all the characteristics of both a parallelogram and a kite? A parallelogram, a trapezium, a rhombus, a rectangle, and more
25. which one possesses all the characteristics of both a parallelogram and a kite? A parallelogram, a trapezium, a rhombus, a rectangle, and more
Explanation:
Rhombus (b)
Each characteristic of a rhombus is shared by a parallelogram and a kite.
26. A quadrilateral's angles have the following proportions: 1: 2: 3: 4. It is the smallest angle.
A 72°, B 144°, C 36°, D 18°
26. A quadrilateral's angles have the following proportions: 1: 2: 3: 4. It is the smallest angle.
A 72°, B 144°, C 36°, D 18°
Explanation:
(c) 36°
We are aware that the total interior angle of all quadrilaterals is 360 degrees. Assume that there are four angles: x, 2x, 3x and 4x.
Then,
x + 2x + 3x + 4x = 360°
10x = 360°
x = 360/10
x = 36
The angles are therefore x = 36°.
2x=2×36=72°
3x=3×36=108°
4x=4×36=144°
27. The measure of D in the trapezium ABCD is
A 55°, B 115°, C 135°, D 125°
27. The measure of D in the trapezium ABCD is
A 55°, B 115°, C 135°, D 125°
Explanation:
(d) 125o
When looking at the provided figure, D and A are supplemental.
We are aware that the total additional angle is 180 degrees.
Consequently, D + A = 180°
∠D + 55o = 180o
∠D = 180o – 55o
∠D = 125o
28. There are three sharp angles on a quadrilateral. If each is 80°, then the fourth angle's measurement is
105°, 150°, 120°, 120°, 105°, 140°
28. There are three sharp angles on a quadrilateral. If each is 80°, then the fourth angle's measurement is
105°, 150°, 120°, 120°, 105°, 140°
Explanation:
(b) 120o
We are aware that the total interior angle of all quadrilaterals is 360 degrees. Assume that the fourth angle is X.
Then,
80°+80°+80°+X=360°
240°+X=360°
X=360°-240°
X=120°
29. A regular polygon has 29 sides if each exterior angle measures 45 degrees. (a) 8 (b) 10 (c) 4 (d) 6
29. A regular polygon has 29 sides if each exterior angle measures 45 degrees. (a) 8 (b) 10 (c) 4 (d) 6
Explanation:
(a) 8
Let's now assume that a normal polygon has n sides.
The total external angle of all polygons, according to WKT, is 360 degrees. It is assumed from the question that each external angle is 45 degrees in length. Then,
n×45°=360°
n=360°/45°
n = 8
30. If P = 60 degrees in a parallelogram PQRS, then the other three angles are (a) 45°, 135°, and 120° ,
(b) 60°, 120°, and 120°
(c) 45°, 135°, 135°
(d)(60°, 135°, 135°)
30. If P = 60 degrees in a parallelogram PQRS, then the other three angles are (a) 45°, 135°, and 120° ,
(b) 60°, 120°, and 120°
(c) 45°, 135°, 135°
(d)(60°, 135°, 135°)
Explanation:
(b) 60o, 120o, 120o
P and Q in a parallelogram are supplementary.
We are aware that the total additional angle is 180 degrees.
P+Q=180° then
∠60o + ∠Q = 180o
∠P = 180o – 60o
∠P = 120o
In a parallelogram, the opposing angles P and R are also equal. So, ∠P = ∠R = 60o
∠Q = ∠S = 120o
Thus, the other three parallelogram angles are 60°, 120°, and 120°.
