∠ A O B is bisected by the ray O C and ray O D is opposite to the ray O C . Prove that ∠ A O D and ∠ B O D are equal.

Given, ∠ A O B is bisected by the ray O C and ray O D is opposite to the ray O C . To prove: ∠ A O D = ∠ B O D Prove: ∠ C O D is a straight angle. Therefore, ∠ A O C + ∠ A O D = 180 ° ⇒ ∠ A O C = 180 ° - ∠ A O D And ∠ C O B + ∠ B O D = 180 ° ⇒ ∠ C O B = 180 ° - ∠ B O D Given, ∠ A O C = ∠ C O B ⇒ 180 ° - ∠ A O D = 180 ° - ∠ B O D ⇒ ∠ A O D = ∠ B O D Hence, proved.

E M B I B E

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.1>Q 4

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IMPORTANT

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Prove that the bisectors of two adjacent supplementary angles include a right angle.

Important Questions on Lines and Angles

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IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.1>Q 5

In the

△ A B C, ∠ A B C = ∠ A C B

. If the side

B C

is produced both ways, prove that the exterior angles are equal.

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IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.1>Q 6

∠ A O B

is bisected by the ray

O C

and ray

\Rightarrow (∠ B E A + ∠ B E C) = \frac{180 °}{2}

is opposite to the ray

O C

. Prove that

∠ A O D

and

∠ B O D

are equal.

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Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.2>Q 1

In the adjoining figure, find the value of $x$ .

Question Image

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Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.2>Q 2

In the adjoining figure, $∠ A O C = (2 y - 13) °$ and $∠ B O C = (3 y - 12) °$ , find all the four angles.

Question Image

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Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.2>Q 3

Prove that the bisectors of a vertically opposite angles are in the same straight line.

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Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.2>Q 4

If two straight lines intersect each other, prove that the ray opposite to the bisector of one angles thus formed bisects the vertically opposite angle.

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Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.3>Q 5

Prove that lines which are perpendicular to the same line are parallel to one another.

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IMPORTANT

Mathematics for Class 9>Chapter 6 - Lines and Angles>EXERCISE 6.3>Q 6

Two unequal angles of a parallelogram are in the ratio