Geometry angles

Question

If QS bisects PQR, m PQS=(7×-6)° and m SQR= (4x +15)° find m PQT

Answer 1

The word "bisect" means to cut in half. So, we have a large angle "PQR" that is cut in half by line "QS". This bisect creates two different angles "PQS" and "SQR". These two smaller angles make up the larger angle. So if the larger angle was cut exactly in half, the two smaller angles should equal each other:

PQS = SQR

7x - 6 = 4x + 15

-4x

3x - 6 = 15

+6 +6

3x = 21

x = 7

Your question says to find "PQT" but since there's no "T" in the problem I'm assuming it wants us to find "PQR". To do this, just plug 7 in for x for both of the smaller angles, add them up, and that will be your answer.

(7*7 - 6) + (4*7 + 15)

(49 - 6) + (28 + 15)

43 + 43

86