Answer :
Answer:
The Proof is given below.
Step-by-step 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
∴ [tex]m \angle ROS + m\angle SOQ = 180\°[/tex]
As the SUM of both the angles is 180° therefore they are supplementary angles.
