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Question

Find the measure of y in the given figure.

  1. 80
  2. 60
  3. 30
  4. 45


Solution

The correct option is C 30
Given: PQ = QR = RP = RS

Here, PQR is an equilateral triangle because all sides are equal in length.
Therefore, each angle measures 60.

Since PRS is an exterior angle to PQR,
PQR+QPR=PRS=x
x=60+60
x=120

In PRS,
RS = PR (Given)
  PRS is an isosceles triangle.
RPS=RSP
(Base angles of an isosceles triangle)

In PRS,
 PRS+RSP+SPR=180
(Sum of all the interior angles of a triangle is 180)
x+y+y=180
x+2y=180
2y=180120
2y=60
y=30

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