Question

In a trapezium the base angles are equal. The remaining angles are twice the measure of base angles. Find the value of one base angle.

• A. 30°
• B. 60°
• C. 90°
• D. 120°

Answer 1

The correct option is B 60°


Let the measure of each base angle be x.
$\angle$ADC = $\angle$BCD = x.
$\angle$BAD = $\angle$ABC = 2x (Given)

$\angle$ADC + $\angle$BCD + $\angle$BAD +$\angle$ABC = 360° (Angle sum property of a quadrilateral)
$\Rightarrow$ x + x + 2x + 2x = 360°.
$\Rightarrow$ 6x = 360°.
$\Rightarrow$ x = $\frac{360°}{6}$ = 60°.
$\Rightarrow$ x = 60°

The value of base angle is 60°.