Question

O is the centre of a circle. $\widehat{ABC}=\theta$ then $x^o+y^o$ is

• A. $180-\theta$
• B. $90+\theta$
• C. $\frac{3\theta }{2}$
• D. $180+\theta$

Answer 1

The correct option is D $180+\theta$

Angle at centre $=2\times$ angle at circumference
$\Rightarrow x=2\theta$ In a cycle quadraliteral ABCD,
$\angle y+\theta ={180}^o\Rightarrow y=180-\theta \Rightarrow x+y=180+\theta$.