Question

Three angles of a quadrilateral are equal. If the fourth angle is ${69}^{\circ }$, find the measure of equal angles.

• A. ${86}^o$
• B. ${97}^o$
• C. ${68}^o$
• D. None of the above

Answer 1

Answer: (B)

${97}^o$

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

Given, three angles are equal. Let the measure of each of these angles be $x$.

Also, fourth angle $={69}^o$.
Then, $x+x+x+{69}^o={360}^o$

$\Rightarrow 3x+{69}^o={360}^o$.

$\Rightarrow$ $3x={360}^o-{69}^o$

$\Rightarrow$ $3x={291}^o$

$\Rightarrow x=\frac{{291}^o}{3}={97}^o$.

Therefore, the equal angles are each $={97}^o$.

Hence, option $B$ is correct.