Question

Three angles of a quadrilateral are equal. Fourth angle is of measure ${150}^{\circ }$. What is the measure of equal angles.​

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Answer 1

Step: Find the measure of equal angles​

Given : Three angles are equal in measure
Fourth angle $={150}^{\circ }$

Let the measure of three equal angles be $x^{\circ }$ each

According to angle sum of property of quadrilateral,
Sum of the interior angles of a quadrilateral is ${360}^{\circ }$.

$\Rightarrow x^{\circ }+x^{\circ }+x^{\circ }+{150}^{\circ }={360}^{\circ }$
$\Rightarrow 3x^{\circ }+{150}^{\circ }={360}^{\circ }$
$\Rightarrow 3x^{\circ }={210}^{\circ }$
$\Rightarrow x^{\circ }={70}^{\circ }$

Hence, the measure of three equal angles is ${70}^{\circ }$ each.