Answers:
angle RQS = 101 degrees
angle TQS = 79 degrees
===================================================
Step-by-step explanation:
A straight angle has a measure of 180 degrees. It's another way of saying "straight line".
The two angles shown add to 180.
We'll use this fact to solve for x.
(angleRQS) + (angleTQS) = angle RQT
(9x+2) + (7x+2) = 180
16x+4 = 180
16x = 180-4
16x = 176
x = 176/16
x = 11
Use this x value to determine the angles we're after.
- angle RQS = 9x+2 = 9*11+2 = 99+2 = 101 degrees
- angle TQS = 7x+2 = 7*11+2 = 77+2 = 79 degrees
Check:
(angleRQS) + (angleTQS) = 101+79 = 180 which confirms the answer is correct.