Question

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

• A. 45${}^{\circ }$, 75${}^{\circ }$, 105${}^{\circ }$ and 135${}^{\circ }$
• B. 25${}^{\circ }$, 90${}^{\circ }$, 105${}^{\circ }$ and 155${}^{\circ }$
• C. 75${}^{\circ }$, 65${}^{\circ }$, 105${}^{\circ }$ and 145${}^{\circ }$
• D. 75${}^{\circ }$, 45${}^{\circ }$, 175${}^{\circ }$ and 85${}^{\circ }$

Answer 1

The correct option is A 45${}^{\circ }$, 75${}^{\circ }$, 105${}^{\circ }$ and 135${}^{\circ }$

Let,the measures of the angles be 3x${}^{\circ }$, 5x${}^{\circ }$, 7x${}^{\circ }$ and 9x${}^{\circ }$.

Sum of all the angles of a quadrilateral is ${360}^{\circ }$.
$\Rightarrow$ 3x${}^{\circ }$ + 5x${}^{\circ }$ + 7x${}^{\circ }$ + 9x = 360${}^{\circ }$
$\Rightarrow$ 24x${}^{\circ }$ = 360${}^{\circ }$
$\Rightarrow$ x${}^{\circ }$ = 15${}^{\circ }$​
Angles measure:
$3\times 15$${}^{\circ }$ = 45${}^{\circ }$
$5\times 15$${}^{\circ }$ = 75${}^{\circ }$
$7\times 15$${}^{\circ }$ = 105${}^{\circ }$
$9\times 15$${}^{\circ }$ = 135${}^{\circ }$