Question

One of the angles of a triangle is 120∘ and the other two angles are equal. Find the measure of each of the equal angles. a) 30∘, 30∘ b) 40∘, 40∘ c) 45∘, 45∘ d) 50∘, 50​

Answer 1

a) 30°, 30°

Explanation:

Let's denote the equal angles in the triangle as x degrees each.

Given:

One angle = 120 degrees

Two angles are equal = x degrees each

In a triangle, the sum of all angles is always 180 degrees. So, we can set up an equation:

120 degrees (given angle) + x degrees (equal angle) + x degrees (equal angle) = 180 degrees

Now, solve for x:

120 degrees + 2x degrees = 180 degrees

Subtract 120 degrees from both sides:

2x degrees = 180 degrees - 120 degrees

2x degrees = 60 degrees

Now, divide both sides by 2 to find the value of x:

x degrees = 60 degrees / 2

x degrees = 30 degrees

So, each of the equal angles in the triangle measures 30 degrees.

The correct answer is option (a) 30°, 30°.