Question

C) Prove that the angles ROS and SOQ are
supplementary.​

Answer 1

The Proof is given below.

Explanation:

Supplementary Angles:

Supplementary angles are those angles when they add up to 180°.

Example: 37° and 143° are supplementary angles. Because the sum is 180°

Given:

∠ ROS and ∠ SOQ are two angles with OS as a common ray as shown in the figure.

To Prove:

∠ ROS + ∠ SOQ = 180°

Proof:

In the figure R-O-Q is a straight line.

Ray OS is common arm to both the angles that is ∠ ROS and ∠ SOQ.

Now In Linear Pair postulate, a straight line forming two adjacent angles with common vertex and one common ray then the sum of two adjacent angles is 180°

Here the straight line is R-O-Q

common vertex O

common ray OS

∴
`m \angle ROS + m\angle SOQ = 180\°`

As the SUM of both the angles is 180° therefore they are supplementary angles.