Question

a) In APQR, PR is extended to S, as shown in Fig. 3. If ZQ = x + 50, ZP = 2x, and
ZQRS = 4x + 30, find the measure of ZQRP in degrees.
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Answer 1

Using exterior interior property of a triangle

ZQ + ZP = ZQRS

x+50 + 2x = 4x+30

2x + 50 - 30 = 4x - x

2x + 20 = 3x

20 = 3x - 2x

x = 20

therefore,

ZQRP + ZQRS = 180° (Linear Pair)

ZQRP + 4x + 30 = 180°

ZQRP + 4×20 + 30 = 180°

ZQRP + 80 + 30 = 180°

ZQRP = ( 180 - 80 - 30 )°

ZQRP = 70°

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