Question

Find the value of x in the following quadrilateral.

• A. 85°
• B. 95°
• C. 90°
• D. 185°

Answer 1

The correct option is A 85°

Any quadrilateral can be divided into 2 triangles. So, the sum of the measures of internal angles of a quadrilateral is equal to the sum of the measures of internal angles of two triangles, i.e., 360°.


So, in quadrilateral ABCD, we can see,



$\angle ABC+\angle BCA+\angle CDA+\angle DAB=360°$

$\Rightarrow (x+5{)}^{\circ }+(x+5{)}^{\circ }+(x+5{)}^{\circ }$
$+(x+5{)}^{\circ }={360}^{\circ }$

$\Rightarrow 4x+{20}^{\circ }={360}^{\circ }$

$\Rightarrow 4x={360}^{\circ }-{20}^{\circ }={340}^{\circ }$

$\Rightarrow x=\frac{{340}^{\circ }}{4}={85}^{\circ }$

So, the value of x is 85°.