Question

If the angles of the quadrilateral are in the ratio 4:5:3:6; find the measure of each angle.

• A. ${90}^{\circ }$, ${100}^{\circ }$, ${60}^{\circ }$ and ${110}^{\circ }$
• B. ${90}^{\circ }$, ${110}^{\circ }$, ${65}^{\circ }$ and ${80}^{\circ }$
• C. ${86}^{\circ }$, ${100}^{\circ }$, ${54}^{\circ }$ and ${120}^{\circ }$
• D. ${80}^{\circ }$, ${100}^{\circ }$, ${60}^{\circ }$ and ${120}^{\circ }$.

Answer 1

The correct option is D ${80}^{\circ }$, ${100}^{\circ }$, ${60}^{\circ }$ and ${120}^{\circ }$.

Let us consider the angles of the quadrilateral to be 4x, 5x, 3x and 6x.

We know,

The sum of angles of quadrilateral = ${360}^{\circ }$
4x + 5x + 3x + 6x = ${360}^{\circ }$
18x = ${360}^{\circ }$
x = $\frac{{360}^{\circ }}{18}$

We get,
x = ${20}^{\circ }$

Now, the measure of angles are,
4x = 4 × ${20}^{\circ }$ = ${80}^{\circ }$
5x = 5 × ${20}^{\circ }$ = ${100}^{\circ }$
3x = 3 × ${20}^{\circ }$ = ${60}^{\circ }$
6x = 6 × ${20}^{\circ }$= ${120}^{\circ }$

Therefore, the angles of the quadrilateral are ${80}^{\circ }$, ${100}^{\circ }$, ${60}^{\circ }$ and ${120}^{\circ }$.