Question

If the measures of angles of a quadrilateral are in the ratio 2 : 5 : 8 : 9, then their measures in radians, will be

(A) \(\frac{\pi^c}6\),\(\frac{5\pi^c}{12}\),\(\frac{3\pi^c}2\),\(\frac{3\pi^c}4\)

(B) \(\frac{\pi^c}3\),\(\frac{5\pi^c}{12}\) ,\(\frac{2\pi^c}3\),\(\frac{2\pi^c}5\)

(C)  \(\frac{\pi^c}6\),\(\frac{5\pi^c}{12}\) ,\(\frac{2\pi^c}3\),\(\frac{4\pi^c}3\)

(D)  \(\frac{\pi^c}6\),\(\frac{5\pi^c}{12}\) ,\(\frac{2\pi^c}3\),\(\frac{3\pi^c}4\)

Answer 1

(D)  \(\frac{\pi^c}6\),\(\frac{5\pi^c}{12}\) ,\(\frac{2\pi^c}3\),\(\frac{3\pi^c}4\)

Let the measure of the angles be 2k, 5k, 8k and 9k in radians. 

∴ 2k + 5k + 8k + 9k = 2π

 ….[∵ the sum of the measures of the angles of a quadrilateral is 2π^c]

⇒ 24k = 2π

⇒ k = π/12

∴ Measures of angles of the quadrilateral are

\(\frac{\pi^c}6\),\(\frac{5\pi^c}{12}\) ,\(\frac{2\pi^c}3\),\(\frac{3\pi^c}4\)