Question

Find the value of $x$ in the given figure.

Answer 1

Hint: Using polygon formula to find missing angle and then find.This polygon is a pentagon and we find the value of $\mathrm{\angle }1$ further, we will find the value of x.

Formula used: Sum of angles in a pentagon is $${540}^{\circ }$$ i.e. $\mathrm{\angle }1+\mathrm{\angle }2+\mathrm{\angle }3+\mathrm{\angle }4+\mathrm{\angle }5={540}^o$.

Complete step by step answer:
(1) Given angles of pentagon are: $${108}^{\circ },{90}^{\circ },{120}^{\circ },{100}^{\circ },\mathrm{\angle }1$$
We know sum of all five angles of a pentagon is $${540}^{\circ }.$$
(2) Calculating sum of all five angles $${108}^{\circ }+{90}^{\circ }+{120}^{\circ }+{100}^{\circ }+\mathrm{\angle }1={540}^{\circ }$$
$$\Rightarrow {418}^{\circ }+\mathrm{\angle }1={540}^{\circ }$$
$$\Rightarrow \mathrm{\angle }1\text{ = }{540}^{\circ }-{418}^{\circ }$$
$$\therefore \mathrm{\angle }1={122}^{\circ }\dots \dots \left(i\right)$$
 (3) From the figure, we see that $\mathrm{\angle }1$ and $x$ are linear pairs.
from equation (i)
$$\therefore \mathrm{\angle }1+x={180}^{\circ }$$
$$\Rightarrow {122}^{\circ }+x={180}^{\circ }$$
$$\Rightarrow x={180}^{\circ }-{122}^{\circ }$$
$$\therefore x={58}^{\circ }$$
Therefore, the value of $$x$$ is $${58}^{\circ }$$ .

Note: Sum of angles of every polygon is fixed and it depends upon the number of sides of the polygon. In geometry, a pentagon is a five sided polygon with five straight sides and five interior angles that sum up to $${540}^{\circ }$$. A pentagon shape is a plane figure, or flat (two-dimensional) 5- sided geometric shape.