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Question

If ray QS bisects angle PQT, m angle SQT = (8×-25) degrees, m angle PQT = (9×+34) degrees, and m angle SQR = 112 degrees, find each:

X =

M angle PQS

M angle PQT

M angle TQR

Answer 1

Since ray QS bisects <PQT, then m<PQS = m<SQT = 8x-25.

m<PQT = m<PQS + m<SQT

9x+34 = 8x - 25 + 8x - 25

84 = 7x

x = 12

so m<PQS = 8(12) - 25 = 71

since m<SQT = m<PQS, m<SQT = 71

and m<PQT = m<PQS + m<SQT = 71 + 71 = 142

m<TQR = m<SQR + m<SQT

= 112 + 71 = 183