Question

Using the information given below in the figure, find the measures of ∠XYQ, & ∠PXZ.​

Answer 1

O=centre

Angles subtended by a chord are equal

Therefore <XPY = <XQY

So... <XQY = 45

Angles in a triangle sum up to 180

<PZX + <ZXP + <XPZ = 180

75 + <ZXP + 45 = 180

120 + <ZXP = 180

180 - 120 = <ZXP

60 = <ZXP

Angles in a triangle sum up to 180

<XYQ + <YQX + <QXY = 180

<XYQ + 45 + 50 = 180

<XYQ + 95 = 180

180 - 95 = <XYQ

85 = < XYQ

ANSWER:- <XYQ = 85, <PXZ = 60, <YQX = 45