Question

Find x in the given figure.

Answer 1

Hint: In the given question we are given a figure in which we need to find the value of angle x and two other angles are given. We can clearly see that we need to use the angle sum property and then find the value. The total angle is taken to be ${{360}^{\circ }}$ .

Complete step-by-step solution:

So, from the given figure we can see that the total angle is divided into three angles as ${{100}^{\circ }},{{123}^{\circ }}$ and we are asked to find the third angle which is taken as a variable x.
We know that the total angle makes an angle of ${{360}^{\circ }}$. So, we can directly calculate this by subtracting the sum of two angles from ${{360}^{\circ }}$ and what we will attain is going to be the third angle x or we can say that the obtained value would be the measure of angle x.
Mathematically it would be done as,
$\begin{align}
  & {{360}^{\circ }}={{100}^{\circ }}+{{123}^{\circ }}+x \\
 & \Rightarrow x={{360}^{\circ }}-\left( {{100}^{\circ }}+{{123}^{\circ }} \right) \\
 & \Rightarrow x={{360}^{\circ }}-{{223}^{\circ }} \\
 & \Rightarrow x={{137}^{\circ }} \\
\end{align}$
Therefore, the third angle of the given figure is ${{137}^{\circ }}$. This implies the value of x is 137.

Note: In the given question we need to be aware of some angle sum property in order to evaluate other angles we are provided with few angles and need to compute the other angles. Apart from this we need to observe the figure and the shape of the figure wisely as it sometimes includes shape property also to find the remaining angles if some are known.