Question

Find the measure of $y$ in the given figure.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

In $\Delta$PQR is an equilateral triangle

$\angle PRQ={60}^o$

$\angle PRS+\angle PRQ={180}^o$

(angle sum)

$x+60=180$

$x={120}^o$ …………$\left(1\right)$

In $\Delta$PRS

$y+y+x=180$

$2y+x=180$

from equation $\left(1\right)$

$2y=180-120=60$

$y={30}^o$.