Question

The angles A, B, C, D of a quadrilateral are in the ratio 3:4:5:8 respectively. The value of angle C is.

• A. ${90}^{\circ }$
• B. ${54}^{\circ }$
• C. ${72}^{\circ }$

Answer 1

The correct option is A ${90}^{\circ }$

The angles of a quadrilateral are in the ratio 3:4:5:8.
Let the angles of the quadrilateral be $3x,4x,5x,8x.$
Sum of angles of the quadrilateral is ${360}^{\circ }.$
$\Rightarrow 3x+4x+5x+8x={360}^{\circ }$
$\Rightarrow 20x={360}^{\circ }$
$\Rightarrow x={18}^{\circ }$
$\therefore \angle A=3x={54}^{\circ },\angle B=4x={72}^{\circ },\angle C=5x={90}^{\circ },\angle D=6x={144}^{\circ }$