Q. 104.2( 6 Votes )

An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are
A. 48°, 60°, 72°

B. 50°, 60°, 70°

C. 52°, 56°, 72°

D. 42°, 60°, 76°

Answer :

Let 1, 2 and 3 be the angles of the triangle and 4 be its exterior angle.

4 = 1080 (Given)


1: 2 = 4: 5 (Given)


Let, 1 = 4k


2 = 5k


Now,


1 + 2 = 108o (Exterior angle theorem)


4k + 5k = 108o


9k = 108o


k = 12o


Thus,


1 = 4 * 12 = 48o


2 = 5 * 12 = 60o


We know that,


1 + 2 + 3 = 180o


48o + 60o + 3 = 180o


108o + 3 = 180o


3 = 180o – 108o


= 72o


Thus, angles of triangle are 48o, 60o, 72o.

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