Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 4

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9th Manipur Board

IMPORTANT

Earn 100

In any regular polygon of $n$ sides, prove that each of its angles measures $\frac{(n - 2)}{n} \times 180 °$ .

Important Questions on Lines and Angles

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9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 5

The sides

A B and A C

of the

∆ A B C

are produced to

P and Q

respectively. The bisectors of

∠ P B C and ∠ Q C B

intersects at

O

. Prove that

∠ B O C = 90 ° - \frac{1}{2} ∠ B A C

.

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9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 6

An exterior angle of a triangle is

120 °

and one of the interior opposite angles is

20 °

. Find the other two angles of the triangle.

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9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 7

A B C

is a triangle. The bisector of the exterior angle at

B

and the bisector of

∠ C

intersect each other at

D

. Prove

∠ B D C = \frac{1}{2} ∠ A

.

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9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 8

In a

∆ A B C, A D

bisects

∠ A and ∠ C > ∠ B

. Prove that

∠ A D B > ∠ A D C

.

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IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 9

The side

B C

of a

∆ A B C

is produces to

D

to form the exterior angle

∠ A C D

. The bisector of

∠ B A C

at

B C at E

. Prove that

∠ A B C + ∠ A C D = 2 ∠ A E C

.

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9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.4>Q 10

A B C

is an isosceles triangle in which

A B = A C

and

A E

bisects the exterior angle

C A D at A

. Prove that

A E ∥ B C

.