Question

Three angles of a quadrilateral measure ${56}^{\circ },{100}^{\circ }$ and ${88}^{\circ }.$ Find the measure of the fourth angle.

• A. ${106}^{\circ }$
• B. ${116}^{\circ }$
• C. ${126}^{\circ }$
• D. ${96}^{\circ }$

Answer 1

The correct option is B ${116}^{\circ }$

Let the measure of the fourth angle be $x^{\circ }$.
${56}^{\circ }+{100}^{\circ }+{88}^{\circ }+x^{\circ }={360}^{\circ }[\because$ Sum of all the angles of quadrilateral is ${360}^{\circ }]$
$\Rightarrow {244}^{\circ }+x={360}^{\circ }$
$\Rightarrow x={360}^{\circ }–{244}^{\circ }={116}^{\circ }$