Question

Find $x$ in the following figure:

Answer 1

Hint: Here we use the exterior angle property. In a polygon Sum of exterior angles is 360.

Complete step by step solution:

We know that , Sum of all exterior angles of any polygon $={360}^{\circ }$

(a) In figure (a) we have,

${125}^{\circ }+{125}^{\circ }+x={360}^{\circ }$

On solving the above equation we get $x$ as

$x={360}^{\circ }-{250}^{\circ }={110}^{\circ }$

Hence the value of $x$ is ${110}^{\circ }$.

(b) Similarly we do here in figure (b),

$x+{75}^{\circ }+{60}^{\circ }+{90}^{\circ }+{90}^{\circ }={360}^{\circ }$

On solving we get,

$x={45}^{\circ }$

Hence the value of $x$ is ${45}^{\circ }$.

Note: In these types of questions we have to apply properties of exterior angle as the angle we have to find is also exterior. By doing this we can get the correct answer.