Question

In the given figure, if $\angle ABC={35}^o$, then the value of $\angle ACB$ is equal to:

• A. ${55}^o$
• B. ${50}^o$
• C. ${45}^o$
• D. ${54}^o$

Answer 1

The correct option is A ${55}^o$

In given figure $ABCD$ is a rectangle and $BC$ passes through center of circle $O$

Then $BOC$ is the diameter of circle

We know Diameter $BOC$ put an angle at any point of semicircle is right angle

Then $\angle BAC={90}^o$

$\angle ABC={35}^o$(GIven)

In $\Delta ABC$

$\angle BAC+\angle ABC+\angle ACB={180}^0$

$\Rightarrow 90+35+\angle ACB=180$

$\Rightarrow \angle ACB=180-90-35=55$

Then $\angle ACB={55}^0$