Question

If two lines intersect such that four vertical angles are equal, then each angle is:

• A. ${45}^{\circ }$
• B. ${100}^{\circ }$
• C. ${180}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$

Let each vertical angle be $x$

Now the sum of vertical angles is ${360}^{\circ }$

$\Rightarrow x+x+x+x={360}^{\circ }\Rightarrow 4x={360}^{\circ }\Rightarrow x=\frac{{360}^{\circ }}{4}={90}^{\circ }$

So option $D$ is correct.