Question

The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of greatest of four angles. *



160 degrees

170 degrees

185 degrees

90 degrees​

Answer 1

$\huge \bf \: 160 \degree$

Sum of all sides of quadrilateral = 360 ° .

$\bf \implies2x + 3 x+ 5x + 8x = 360 \degree \\ \\ \bf \implies18x = 360 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf \implies x = \cancel \frac{360}{18} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf \implies x =20 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf \therefore \: Greatest \: angle = 8x \: \: \: \: \: \: \: \: \: \: \\ \\ \bf \implies8 \times 20 \degree = 160 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$