Question

In the figure , find the value of $x$ .

Answer 1

The sum of the exterior angles of a regular polygon will always equal ${360}^o.$

So, Sum of all the exterior angles of a pentagon $={360}^{\circ }$

${92}^{\circ }+{20}^{\circ }+{85}^{\circ }+x^{\circ }+{89}^{\circ }={360}^{\circ }$

${286}^{\circ }+x^{\circ }={360}^{\circ }$

$x^{\circ }={360}^{\circ }-{286}^{\circ }={74}^{\circ }$