Question

In given figure if $\angle 3={135}^o$, then the value of $\angle 1+\angle 4$ is

• A. ${90}^o$
• B. ${10}^o$
• C. ${45}^o$
• D. ${135}^o$

Answer 1

The correct option is A ${90}^o$

From the figure

$\angle 2=\angle 3={135}^{\circ }$ $(\because verticallyoppositeangles)$

and also

sum of angles at a point is ${360}^{\circ }$

$⟹\angle 1+\angle 2+\angle 3+\angle 4={360}^{\circ }$

$⟹\angle 1+\angle 4={360}^{\circ }-\angle 2-\angle 3={360}^{\circ }-{135}^{\circ }-{135}^{\circ }={90}^{\circ }$