Question

Find the value of $x$ in each figure.

• A. ${65}^{\circ }$
• B. ${70}^{\circ }$
• C. ${105}^{\circ }$

Answer 1

The sum of the interior angles of a quadrilateral is equal to ${360}^{\circ }$. Hence,

$1.\Rightarrow {85}^{\circ }+{105}^{\circ }+{105}^{\circ }+x={360}^{\circ }$
$\Rightarrow {295}^{\circ }+x={360}^{\circ }$
$\Rightarrow x={360}^{\circ }-{295}^{\circ }$
$\Rightarrow x={65}^{\circ }$

$2.\Rightarrow {110}^{\circ }+{88}^{\circ }+{92}^{\circ }+x={360}^{\circ }$
$\Rightarrow {290}^{\circ }+x={360}^{\circ }$
$\Rightarrow x={360}^{\circ }-{290}^{\circ }$
$\Rightarrow x={70}^{\circ }$

$3.\Rightarrow {75}^{\circ }+{75}^{\circ }+{105}^{\circ }+x={360}^{\circ }$
$\Rightarrow {255}^{\circ }+x={360}^{\circ }$
$\Rightarrow x={360}^{\circ }-{255}^{\circ }$
$\Rightarrow x={105}^{\circ }$