Four angles of a quadrilateral are in G.P. Whose common ratio is an intiger. Two of the angles are acute while the other two are obtuse. The measure of the smallest angle of the quadrilateral is Choose the correct answer: A) 12 B) 24 C) 36 D) 46 E) 52
Let the angles be a, ar, ar 2, ar 3.   Sum of the angles = a ( r 4- 1 ) /r -1 = a ( r 2 + 1 ) ( r + 1 ) = 360   a&lt; 90 , and ar&lt; 90, Therefore, a ( 1 + r ) &lt; 180, or ( r 2 + 1 ) &gt; 2   Therefore, r is not equal to 1. Trying for r = 2 we get a = 24   Therefore, The angles are 24, 48, 96 and 192.   ANSWER:24
<result>B</result>
Four angles of a quadrilateral are in G.P. Whose common ratio is an intiger. Two of the angles are acute while the other two are obtuse. The measure of the smallest angle of the quadrilateral is