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 each of them.

• A. ${39}^{\circ }$ and ${16}^{\circ }$
• B. ${30}^{\circ }$ and ${160}^{\circ }$
• C. ${130}^{\circ }$ and ${16}^{\circ }$
• D. ${90}^{\circ }$ and ${126}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$ and ${126}^{\circ }$

Given

Two angles are ${68}^{\circ }$ and ${76}^{\circ }$.

Let us consider the other two angles as 5x and 7x

Hence, ${68}^{\circ }$ + ${76}^{\circ }$ + 5x + 7x = ${360}^{\circ }$

12x + ${144}^{\circ }$ = ${360}^{\circ }$

12x = ${360}^{\circ }$ – ${144}^{\circ }$

12x = ${216}^{\circ }$

x = $\frac{{216}^{\circ }}{12}$ = ${18}^{\circ }$

Now, the other angles are calculated as below:

5x = 5 × ${18}^{\circ }$ = ${90}^{\circ }$

7x = 7 × ${18}^{\circ }$ = ${126}^{\circ }$

Therefore, the values of the other angles are ${90}^{\circ }$ and ${126}^{\circ }$.