Question

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

Answer 1

Construct a line $CD$ to cut the line $AB$ at point $E$.

We know that in the triangle $BDE$ exterior angle is equal to the sum of two opposite interior angles

So we can write it as

$\angle CDB=\angle CEB+\angle DBE$

By substituting the values

$x^{\circ }=\angle CEB+{45}^{\circ }.\left(1\right)$

We know that in the triangle $AEC$ exterior angle is equal to the sum of two opposite interior angles

So we can write it as

$\angle CEB=\angle CAB+\angle ACE$

By substituting the values

$\angle CEB={55}^{\circ }+{30}^{\circ }$

By addition

$\angle CEB={85}^{\circ }$

By substituting $\angle CEB$ in equation (1) we get

$x^{\circ }={85}^{\circ }+{45}^{\circ }$

By addition

$x^{\circ }={130}^{\circ }$.