Question

Three angles of a quadrilateral are equal and the measure of the fourth angle is ${120}^{\circ }$. Find the measure of each of the equal angles.

• A. ${240}^{\circ }$
• B. ${100}^{\circ }$
• C. ${80}^{\circ }$
• D. ${135}^{\circ }$

Answer 1

The correct option is C

${80}^{\circ }$

Let the measure of other equal angles be $x^{\circ }$.

We know that the sum of all the angles of a quadrilateral is ${360}^{\circ }$.

$x^{\circ }+x^{\circ }+x^{\circ }+{120}^{\circ }={360}^{\circ }$

$\Rightarrow {120}^{\circ }+3x={360}^{\circ }$

$\Rightarrow 3x={360}^{\circ }–{120}^{\circ }$

$\Rightarrow 3x={240}^{\circ }$

$\Rightarrow x={80}^{\circ }$

Thus, the measure of other three equal angles is ${80}^{\circ }$.