Question

An exterior angle of a triangle is 120°, and one of
the interior opposite angle is 30°. Find the other two
angles of the triangle.​

Answer 1

Answer:

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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Carter McClung

Answered December 20, 2017

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°

Answer 2

Given:-

• An exterior angle of a triangle is 120°
• One of the interior opposite angle is 30°

To Find:-

• The other two angles of the triangle.

Solution:-

Let 'X' be the interior opposite angle of the ΔXYZ

Let 'Y' be the third angle

⟹ 120° = 30° + ∠X

⟹ ∠X = 90°

We know that:-

Sum of interior angles of a triangle = 180°

⟹ 90° + 30° + ∠Y = 180°

⟹ ∠Y = 180° - 120°

⟹ ∠Y = 60°

• Measure of the first angle = 90°
• Measure of the second angle = 60°

Additional Information:-

• A triangle is a plane closed figure bounded by 3 line segments.
• Vertex of the triangle is a point where two angles meet. A is a vertex of ∠ABC.
• A triangle is denoted by the Greek letter :- [delta]Δ

• Every triangle has three angles ; In the attachment, the three angles are ∠BAC, ∠ABC, ∠ACB.
• The sum of interior angles if a triangle is always equal to 180°.
• In, ΔABC, ∠A + ∠B + ∠C = 180°.

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