Question

One of the exterior angles of a triangle is 112 degree and the corresponding interior opposite angles are in the ratio 3:4. Find the angles of the triangle.

Answer 1

Step-by-step explanation:

One of the exterior angle of a triangle is 112 and the corresponding interior opposite angle are in the ratio of 3:4. What is the angle of triangle?

The exterior angle of a triangle = 112 deg. So its supplementary angle = 180–112 = 68 deg.

The opposite angles are in the ratio of 3:4 and their values are 48 deg and 64 deg.

The three angles of the triangle are 48 deg, 64 deg and 68 deg - a scalene triangle.

Let a ∆ABC

Let the exterior angle C = 112 °

Now interior angle C= 68°

Sum of three angles of ∆ =180°_________(i)

Now , angle A: angle B= 3:4

So let angle A=3x

angle B= 4x

Now using (i)

3x + 4x + 68°= 180°

7x+ 68°= 180°

7x= 112°

x= 16

Now angles are A= 48°

B=64°

C=68°~