Question

(1)An exterior angle of a triangle is 120° and its interior opposite angles are in the ratio 1:3, then the angle are.
options :a).30°, 90°
b).30°, 60°
c).60°, 90°
d).60°, 60°​

Answer 1

please mark as brainlist ans

An exterior angle of a triangle is 120 degrees and one of the interior opposite angles is 30 degrees. What are the other angles of triangles?

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Step one, draw a picture!

There are three relevant theorems to help us here:

The angle sum theorem: a + b + c = 180° (interior angles of a triangle sum to 180°)

The linear pair theorem: b + d = 180° (linear pairs are supplementary)

And by combining the two, and a little Algebra, you get

Exterior angle theorem: a + c = d (The exterior angle is equal to the sum of the two remote interior angles)

In the problem, you were given an exterior angle, d = 120°, and a remote interior angle (a or c, they’re interchangeable).

We know from linear pair theorem that b + 120° = 180°. So b = 60°

We can either use angle sum theorem or exterior angle theorem to find that last bad boy.

Angle sum theorem:

a + 60° + 30° = 180

a = 90°

Exterior angle theorem:

a + 30° = 120°

a = 90°