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Answer 1

Answer:

The correct option is A

Step-by-step explanation:

If AB=BR then angle R = angle A = 29° (angles opposite to equal sides are equal)

therefore in ∆ABR

angle A+ angle B + angle R = 180°

29°+angle B + 29° = 180

angle B= 180-58

angle B= 122°

then,

angle RBA+ angle RBC = 180° (supplementary )

122° + angle RBC= 180°

angle RBC= 58°

x= 58°

in ∆RBX

50°+58°+angle RXB =180

angle RXB = 72°

Angle SRQ= Angle RQP= 32°

and

angle RXB+ angle CXQ = 180°

72°+ angle CXQ =180°

angle CXQ= 108°

In ∆CXQ

108°+32°+z=180°

z=40°

Also, angle ARB+ Angle BRX=angle PRQ

29+50 = 79°

therefore in ∆PRQ

79+y + 32= 180

y=69°