Geometry Homework

Question

QS bisects <PQR. What is m<PQS? PQS is (x+24) and QSR is (3x-36)

Answer 1

Angle PQR is cut in half by the line QS.

The new, equal angles that are formed are PQS and SQR.

m∠PQS = x + 24

m∠SQR = 3x - 36

Since these two angles are equal, we set their values equal and try to solve for x:

x + 24 = 3x - 26

x + 24 = 3x - 26

-x -x

24 = 2x - 26

24 = 2x - 26

/2 /2 /2

12 = x - 13

12 = x - 13

+13 +13

25 = x

Don't forget that we are trying to solve for m∠PQS, not just x!

m∠PQS = x + 24

= 25 + 24

= 49