Q78. - Algebra 2

Question

In triangle PQR, $\overline{QS}$ and $\overline{SR}$ are angle bisectors and angle $P=74°$. How many degrees are there in angle QSR?

A. 106

B. 121

C. 125

D. 127

E. 143

Step-by-Step Solution

Answer

The correct option is D.

Step 1- State the angles without measurement

Name the angles that are without measurement.

Step 2 – Make the equation for triangle QSR

The equation that represents the triangle PQR is $2x+2y+74=180°$.

Isolate the addition of the variables x and y.

$x+y=53$

If the angles x and y are subtracted from 180 then they will result in measurement of triangle QSR so, 

$\begin{array}{c}QSR=180-\left(x+y\right)\\ =180-53\\ =127\end{array}$

Step 3- Make the conclusion

The obtained measurement is 127 which mean that option D is correct.