Question

Mark (✓) against the correct answer:
The angles of quadrilateral are in the ratio 1 : 3 : 7 : 9. The measure of the largest angle is
(a) 63°
(b) 72°
(c) 81°
(d) none of these

Answer 1

(d) none of the these

Let the angles be $\left(x\right)°,\left(3x\right)°,\left(7x\right)°\mathrm{and}\left(9x\right)°$.

Sum of the angles of the quadrilateral is ${360}^{\circ }$.

$$\begin{gathered} x+3x+7x+9x=360 \\ 20x=360 \\ x=18 \end{gathered}$$

$$\begin{gathered} \mathrm{Angles}: \\ \left(3x\right)°=(3\times 18)={54}^{\circ } \\ \left(7x\right)°=(7\times 18)°={126}^{\circ } \\ \left(9x\right)°=(9\times 18)°={162}^{\circ } \end{gathered}$$