c) Prove that the angles ROS and SOQ aresupplementary.
Accepted Solution
A:
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-Qcommon vertex Ocommon 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.