Question

If one angle of a cyclic trapezium is double the other, then the measure of the larger angle is

• A. ${130}^o$
• B. ${125}^o$
• C. ${120}^o$
• D. ${115}^o$

Answer 1

Answer: (C)

${120}^o$

$\Rightarrow$ In given figure ABCD is a cyclic trapezium.

$\Rightarrow$ Let $\angle A=2\angle C$ [Given] ---- (1)

$\Rightarrow$ $\angle$A + $\angle$ C = 180${}^{\circ }$ [$\because$ ABCD beaing a cyclic trapezium]

$\Rightarrow$ 2$\angle$C + $\angle$C = 180${}^{\circ }$ [From (1)]

$\Rightarrow$ 3$\angle$C = 180${}^{\circ }$

$\therefore$ $\angle$C = 60${}^{\circ }$

$\therefore$ Measure of greater angle,

$\angle A=2\times {60}^{\circ }={120}^{\circ }$