# An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle areA. 48°, 60°, 72°B. 50°, 60°, 70°C. 52°, 56°, 72°D. 42°, 60°, 76°

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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