Answer:
m∠RQS = 102°
m∠TQS = 78°
Explanation:
We first have to find "x" to determine what each angle measure is.
Since angles RQS and TQS are linear pairs, they are adjacent angles sharing a side whose uncommon sides add up to 180 degrees.
So, in order to find out what value "x" is, we have to add these two angles and set them equal to 180 degrees.
Given:
∠RQS = 9x + 3
∠TQS = 7x + 1
Now solve:
(9x + 3) + (7x + 1) = 180
Combine like terms:
(9x + 7x) + (3 + 1) = 180
16x + 4 = 180
Get rid of constants.
Inverse operation of addition is subtraction:
16x + 4 = 180
-4 -4
16x = 176
Divide both sides by 16 since inverse operation of multiplication is division:
16x = 176
/16 /16
x = 11
Now that we've found the x-value, all we have to do is just plug it into the expressions given for each angle to find out exactly what their measures are.
∠RQS = 9x + 3
Substitute "x" for 11:
9(11) + 3
99 + 3
102
m∠RQS = 102°
∠TQS = 7x + 1
Substitute "x" for 11:
7(11) + 1
77 + 1
78
m∠TQS = 78°