Question

At the intersection of two lines, out of four angles formed, two adjacent angles are equal. Find all the angles.

• A. ${60}^{\circ }$, ${60}^{\circ }$, ${120}^{\circ }$, ${120}^{\circ }$
• B. ${180}^{\circ }$, ${180}^{\circ }$, $0^{\circ }$, $0^{\circ }$
• C. ${90}^{\circ }$, ${90}^{\circ }$, ${90}^{\circ }$, ${90}^{\circ }$
• D. ${45}^{\circ }$, ${45}^{\circ }$, ${135}^{\circ }$, ${135}^{\circ }$

Answer 1

The correct option is C ${90}^{\circ }$, ${90}^{\circ }$, ${90}^{\circ }$, ${90}^{\circ }$

Sum of adjacent angles at the point of intersection of two lines is ${180}^{\circ }$.

If two adjacent angles are equal then each angle must be $\frac{{180}^{\circ }}{2}$ = ${90}^{\circ }$.

$\Rightarrow$ $\angle AOX=\angle BOX={90}^o$

Since, the vertically opposite angles are equal, so other two angles will also be ${90}^{\circ }$.

$\Rightarrow$ $\angle AOX=\angle BOY={90}^o$
and $\angle BOX=\angle AOY={90}^o$

All the angles are equal to ${90}^o$.