Question

5 3 16 In the given figure, PQ = PR and ZAPR = 110°. Find the measure of ZPQR and - ZQPR. A P 11/0 B. Q R​

Answer 1

Answer:

∠QRP=70°

∠PQR=70°

∠QPR=40°

Step-by-step explanation:

IN QUADRILATERAL APRB

SINCE ABRP IS A QUADRILATERAL

SUM OF INTERIOR ANGLE = 360°

∠APR+∠PRB+∠RBA+∠BAP = 360°

(∠APR=110°) GIVEN

(∠BAP=90°) GIVEN

(∠RBA=90°) GIVEN

110°+∠PRB+90°+90° = 360°

290°+∠PRB = 360°

=  ∠PRB+70°

IN TRIANGLE PQR

SUM OF INTERIOR ANGLE = 180

∠PRQ+∠RQP+∠QPR=180°

SINCE SIDE PQ AND PR ARE EQUAL

THE ANGLES OPPOSITE TO EQUAL SIDE ARE ALSO EQUAL

∠PQR=∠PRQ=70

70°+70°+∠QPR = 180°

140°+∠QPR=180°

∠QPR=40°