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Question

Find the measure of y in the given figure.


A
30
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B
60
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C
90
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D
120
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Solution

The correct option is A 30

Given: PQ = QR = RP = RS
PQR is an equilateral triangle because all sides are equal in length.
Therefore, each angle measures 60.
Using exterior angle property,
PQR + QPR = PRS=x
x=60+60
x=120
In PRS,
RS = PR (Given)
PRS is an isosceles triangle.
Using angle sum property ,
PRS+RSP+SPR=180
x+y+y=180
120+2y=180
2y=180120
2y=60
y=30


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