Question

Consider the following figure.

It is given that $\stackrel{⟷}{PB}$ and $\stackrel{⟷}{RC}$ are parallel lines. Find x

• A. 35°
• B. 55°
• C. 90°
• D. 125°

Answer 1

The correct option is C

90°

$\angle$ ARO = $\angle$ CRY = 55${}^{\circ }$ (vertically opposite angles)
$\angle$ TPB = $\angle$ OAR = 35${}^{\circ }$ (corresponding angles)
Also, in $\Delta$OAR, we have, x + $\angle$ ARO + $\angle$ TPB = 180${}^{\circ }$
x = 180${}^{\circ }$ - (55${}^{\circ }$ + 35${}^{\circ }$)
= 90${}^{\circ }$