Answer:
From the given diagram, the measurement of ∠RQS is 106° and the measurement of ∠TQS is 74°
Step-by-step explanation:
For this problem, we are to find the measurements of ∠RQS and ∠TQS which makes up the straight line RQT. Straight lines have a measurement of 180°. So, since ∠RQS and ∠TQS make up ∠RQT, then we are goingt o set up an equation where we add ∠RQS and ∠TQS together and equal them to ∠RQT.
m∠RQS + m∠TQS = m∠RQT
Now, let's fill the information from the problem into our equation.
(11x + 7) + (8x + 2) = 180
Combine like terms on the left side of the equation.
19x + 9 = 180
Subtract 9 form both sides of the equation.
19x = 171
Divide by 19 on both sides of the equation.
x = 9
So, we know the value of x is 9. Now, let's plug in this value into each angle so we can see the measurements of each.
m∠RQS = 11(9) + 7 = 99 + 7 = 106°
m∠TQS = 8(9) + 2 = 72 + 2 = 74°
