If the measures of angles of a quadrilateral are in the ratio 2 : 5 :

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

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»

(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

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