Question

In the given figure, find $a+b$

Answer 1

$\frac{1}{2}x+5(\frac{x}{2}-1)+x+9={180}^{\circ }$ (sum of angles at a point on a line)

$⟹\frac{x}{2}+\frac{5x}{2}-5+x+9={180}^{\circ }$

$⟹4x+4={180}^{\circ }$

$⟹4x={176}^{\circ }$

$⟹x=\frac{{176}^{\circ }}{4}$

$\therefore x={44}^{\circ }$

We know that, exterior angle is equal to the sum of it's opposite interior angles.

So, $a+b=\frac{1}{2}x+5(\frac{x}{2}-1)$

$=\frac{x}{2}+\frac{5x}{2}-5$

$=3x-5$

$=3\left(44\right)-5$

$={127}^{\circ }$