Question

If, QT is the angle bisector, measure of $\angle$RQT will be equal to ______.

• A. 30°
• B. 60°
• C. 90°
• D. 120°

Answer 1

The correct option is A 30°


Since SQR is a straight line, $\angle$ SQP +$\angle$ PQR = 180°. (Linear pair)
$\Rightarrow$ 120° + $\angle$ PQR = 180°
$\Rightarrow$ $\angle$ PQR = 180° - 120° = 60°---(i)

QT is the angle bisector. (Given)
$\Rightarrow$ $\angle$PQT = $\angle$RQT---(ii)

$\angle$ PQR = $\angle$PQT + $\angle$ RQT
From (i) and (ii), 60° = 2$\times$ $\angle$RQT
$\Rightarrow$ $\angle$ RQT = $\frac{60°}{2}$ = 30°

Hence the value of $\angle$RQT = 30°.