Question

PQ and QR are perpendicular. Point s lies in the interior of angle PQR.if m/angle PQS =4+7a and m angle SQR=9+4a, find m angle PQS

Answer 1

angle PQS = 53°

Explanation:

You want the measure of angle PQS given that right angle PQR is divided into angles PQS = 4+7a and SQR = 9+4a.

Angle addition

The angle addition theorem tells you the whole is the sum of the parts:

∠PQR = ∠PQS +∠SQR

90° = (4 +7a)° +(9 +4a)°

Solution

0 = -77 +11a . . . . . . . . . . divide by ° and subtract 90

7 = a . . . . . . . . . . . . . . add 77 and divide by 11

The measure of angle PQS is ...

∠PQS = (4 +7·7)° = 53°

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