Question

Two angles of a quadrilateral are ${68}^{\circ }$ and ${76}^{\circ }$. If the other two angles are in the ratio $5:7$, find the measure of largest of them.

• A. ${126}^{\circ }$
• B. ${90}^{\circ }$
• C. ${63}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is A ${126}^{\circ }$

We know, by angle sum property, the sum of interior angles of a quadrilateral=${360}^o$.
Given two angles are ${68}^o$ & ${76}^o$ and the other two angles are in the ratio of $5:7$.
Let the other two angles be $5x^o$ & $7x^o$.
Then, $5x^o+7x^o+{68}^o+{76}^o={360}^o$
$\Rightarrow 12x+{144}^o={360}^o$
$\Rightarrow 12x={360}^o-{144}^o={216}^o$
$\Rightarrow x=\frac{{216}^o}{12}={18}^o$.

So unknown angles are $5x=5\times {18}^o={90}^o$

and $7x=7\times {18}^o={126}^o$.

Therefore, the largest angle is ${126}^o$.

Hence, option $A$ is correct.