1. How many lines can pass through five points without ever crossing over one another?
(A) 10 (B) 5 (C) 20 (D) 8
1. How many lines can pass through five points without ever crossing over one another?
(A) 10 (B) 5 (C) 20 (D) 8
Explanation:
(A) 10
The question makes it clear how many lines pass through all five places.
We already know that a line can only be drawn between two points.
Hence, 5 2 is the number of lines that pass through each of the five points.
= 10
2. The angle between two consecutive spokes on a bicycle wheel with 48 spokes is
(A) 5½ (B) 7½ (c) (c) 2/11 (D) 2/15
2. The angle between two consecutive spokes on a bicycle wheel with 48 spokes is
(A) 5½ (B) 7½ (c) (c) 2/11 (D) 2/15
Explanation:
(B) 7½
Bicycle wheels are circular, as is well known.
The wheel's overall angle is 360 degrees.
It is clear from the question that a bicycle wheel has 48 spokes.
The angle between two consecutive spokes is then equal to 360°/48.
= 7.5
= 7½
3. XYZ cannot be written as in Fig. 2.6.
(A) Y, (B) ZXY, (C) ZYX, and (D) XYP
Geometry Chapter 2 Answers from NCERT Exemplar for Class 6
3. XYZ cannot be written as in Fig. 2.6.
(A) Y, (B) ZXY, (C) ZYX, and (D) XYP
Geometry Chapter 2 Answers from NCERT Exemplar for Class 6
Explanation:
(B) ∠ZXY
4. The measure of BPY is given in Fig. 2.7 if point A is moved to point B along ray PX such that PB = 2PA.
greater than 45° (A) and 45° (B)
Less than 45° (C) and 90° (D)
4. The measure of BPY is given in Fig. 2.7 if point A is moved to point B along ray PX such that PB = 2PA.
greater than 45° (A) and 45° (B)
Less than 45° (C) and 90° (D)
Explanation:
(B) 45o
Point A is moved to point B along ray PX in accordance with the criteria stated in the question so that PB = 2PA.
As a result, changing the point "A" has no effect on the point "P."
As a result, 45o is the measure of BPY.
5. In Fig. 2.10, there are triangles in a total of
(A) 10 (B) 12 (C) 13 (D) 14
5. In Fig. 2.10, there are triangles in a total of
(A) 10 (B) 12 (C) 13 (D) 14
Explanation:
(C) 13
There are 13 triangles visible in the image above.
PQV, RQV, VSQ, VUQ, PVR, PSQ, SQU, SQT, TQU, QUR, VSU, VST, and VTU.
6. Which of the following cannot be true for two angles if their combined angle exceeds 180 degrees?
(A) Two acute and one obtuse angles.
(B) Two acute and one reflex angles.
(C) two acute angles in .
(D) Two straight angles are .
6. Which of the following cannot be true for two angles if their combined angle exceeds 180 degrees?
(A) Two acute and one obtuse angles.
(B) Two acute and one reflex angles.
(C) two acute angles in .
(D) Two straight angles are .
Explanation:
(D) Two straight angles are .
As all right angles must add up to 180 degrees, they must all be equal.
7. If the sum of two angles is an obtuse angle, which of the following cannot be true?
(A) Three acute angles and one obtuse angle.
(B) Two right angles and one acute angle.
(C) 2 acute angles .
(D) Two parallel lines are .
7. If the sum of two angles is an obtuse angle, which of the following cannot be true?
(A) Three acute angles and one obtuse angle.
(B) Two right angles and one acute angle.
(C) 2 acute angles .
(D) Two parallel lines are .
Explanation:
(D) Two parallel lines are .
Right angles must all be equal since they must all sum up to 180 degrees.
A right-angle triangle doesn't have an obtuse angle.
Obtuse angles are those that are greater than 90° but less than 180°.
8. Each side of a polygon is a prime integer. The sum of the two least consecutive primes equals the number of sides that it has. The polygon's number of diagonals is
(A) 4 (B) 5 (C) 7 (D) 10
8. Each side of a polygon is a prime integer. The sum of the two least consecutive primes equals the number of sides that it has. The polygon's number of diagonals is
(A) 4 (B) 5 (C) 7 (D) 10
Explanation:
(B) 5
2 and 3 are the two least consecutive prime numbers.
Two-number sum: 2 + 3 Equals 5.
Using the equation = n(n - 3)/2
= 5(5 – 3)/2
= (5 × 2)/2
= 10/2
= 5
9. Fill in the blanks
There are _______ diagonals in a hexagon.
9. Fill in the blanks
There are _______ diagonals in a hexagon.
Explanation:
In a hexagon, there are nine diagonals.
The six sides of a hexagon are well known.
The formula for the number of diagonals is n(n - 3)/2.
= 6(6 – 3)/2
= 6(3)/2
= 18/2
= 9
10. Angles that are greater than 180° but not quite a full angle are referred to as .
10. Angles that are greater than 180° but not quite a full angle are referred to as .
Explanation:
Reflex angles are defined as angles higher than 180° and smaller than full angles.
11. A trapezium's two opposing sides are called its .
11. A trapezium's two opposing sides are called its .
Explanation:
A trapezium's two opposing sides are parallel.
12. Points located inside the triangle PQR in Fig. 2.14 are _____, points located outside are _____, and points located on the triangle itself are .
12. Points located inside the triangle PQR in Fig. 2.14 are _____, points located outside are _____, and points located on the triangle itself are .
Explanation:
In Fig. 2.14, the points O and S are located inside the triangle PQR, N and T are outside, and M, P, Q, and R are located on the triangle itself.
13. A straight angle contains _____ right angles, while a full angle contains _____ right angles.
13. A straight angle contains _____ right angles, while a full angle contains _____ right angles.
Explanation:
Two right angles make up a straight angle, and four make up a full angle.
We are aware that a straight angle creates an angle of 180 degrees.
and right angle creates a 90o angle.
Hence, the number of right angles is equal to 2 (180/90).
We are aware that a full angle is 360 degrees.
Hence, the number of right angles is equal to 4 (360/90).
14. There are _____ common points between the two angles indicated in Fig. 2.18.
14. There are _____ common points between the two angles indicated in Fig. 2.18.
Explanation:
The two angles shown in Fig. 2.18 have two points in common.
P and Q are the points in the provided figure that are shared by all.
15. There are _____ common points between the two angles indicated in Fig. 2.19.
15. There are _____ common points between the two angles indicated in Fig. 2.19.
Explanation:
In the two angles indicated in Fig. 2.19, there is only one common point between them.
The common point in the illustration is A.
16. PQ and RQ in Fig. 2.13 are 5 cm for PQ and 5 cm for QR. If so, PQR is
A right triangle, but one that is not isosceles
(B) a right isosceles triangle
(C) a right triangle that is not isosceles
(D) neither an isosceles nor a right triangle .
16. PQ and RQ in Fig. 2.13 are 5 cm for PQ and 5 cm for QR. If so, PQR is
A right triangle, but one that is not isosceles
(B) a right isosceles triangle
(C) a right triangle that is not isosceles
(D) neither an isosceles nor a right triangle .
Explanation:
(B) a right isosceles triangle
It is clear from the question that PQ RQ, PQ = 5 cm, and QR = 5 cm.
An isosceles triangle has two equal sides, as is well known.
The supplied PQR is an isosceles right triangle as a result.
17. There are _____ common points between the two angles in Fig. 2.20.
17. There are _____ common points between the two angles in Fig. 2.20.
Explanation:
The two angles marked in Fig. 2.20 have three points in common.
P, Q, and R are the common points in the provided figure.
18. Identify any inaccurate statements in the following and identify them: Two rays having a shared endpoint, two line segments with a common endpoint, or a ray and a line segment with a common endpoint are all examples of an angle.
18. Identify any inaccurate statements in the following and identify them: Two rays having a shared endpoint, two line segments with a common endpoint, or a ray and a line segment with a common endpoint are all examples of an angle.
Explanation:
All three of the statements (a), (b), and (c) are false. Two rays' shared starting points create an angle.
19. Can two obtuse angles have a reflex angle as their total (a)? If not, why not?
(b) an entire angle? If not, why not?
19. Can two obtuse angles have a reflex angle as their total (a)? If not, why not?
(b) an entire angle? If not, why not?
Explanation:
(A) Indeed, two obtuse angles added together are always greater than 180 degrees.
For instance, the total of two obtuse angles, such as 135° and 100°, is 235°, which is more than 180°.
(b) No, the total of two acute angles is less than 360° but is greater than 180°. We can see from the example above that 235°, the result of adding 135° and 100°, is larger than 180° but less than 360°.
20. Draw and label each of the ABCDE pentagon's diagonals.
20. Draw and label each of the ABCDE pentagon's diagonals.
Explanation:
A pentagon ABCDE's diagonals are AC, AD, BE, BD, and EC.
