Question

Question 1
Find x in the following figures:

Answer 1

(a)We know the sum of all exterior angles of any polygon is
${360}^{\circ }$
$\Rightarrow {125}^{\circ }+{125}^{\circ }+x={360}^{\circ }$
$\Rightarrow {250}^{\circ }+x={360}^{\circ }$
$\Rightarrow x={110}^{\circ }$

(b) Sum of angles of a pentagon
$=(n-2)\times {180}^{\circ }$
$=(5-2)\times {180}^{\circ }$
$=3\times {180}^{\circ }={540}^{\circ }$

By linear pairs of angles,
$\angle 1+{90}^{\circ }={180}^{\circ }....\left(i\right)\angle 2+{60}^{\circ }={180}^{\circ }....\left(ii\right)\angle 3+{90}^{\circ }={180}^{\circ }....\left(iii\right)\angle 4+{70}^{\circ }={180}^{\circ }...\left(iv\right)\angle 5+x={180}^{\circ }...\left(v\right)$

Adding eq. (i), (ii), (iii), (iv), and (v),
$x+(\angle 1+\angle 2+\angle 3+\angle 4+\angle 5)+{310}^{\circ }=900\Rightarrow x+{540}^{\circ }+{310}^{\circ }={900}^{\circ }\Rightarrow x+{850}^{\circ }={900}^{\circ }\Rightarrow x={900}^{\circ }-{850}^{\circ }={50}^{\circ }$