Answer:
m∠RQS = 108°
m∠SQT = 72°
Explanation:
Angles RQS and TQS are linear pairs, meaning they both share a common side and have uncommon sides whose angles sum up to 180°(straight angle).
Let's add these two angle's expressions and set them equal to 180°.
(9x + 9) + (6x + 6) = 180
Combine like terms:
(9x + 6x) + (9 + 6) = 180
15x + 15 = 180
-15 -15
15x = 165
/15 /15
x = 11
Now, plug in x for both angle's expressions,
∠RQS = 9x + 9
Substitute "x" for 11:
∠RQS = 9(11) + 9
∠RQS = 99 + 9
m∠RQS = 108°
∠SQT = 6x + 6
Substitute "x" for 11:
∠SQT = 6(11) + 6
∠SQT = 66 + 6
m∠SQT = 72°