Solving Triangle Angle Problems Using Algebra

Published on May 8, 2026

Geometry

Learn how to find the measure of an angle in a triangle by setting up and solving an algebraic equation based on the sum of angles in a triangle.

Question

The problem asks for the measure of angle C in triangle ABC.
We are given the measures of the angles in terms of x:
Angle A =

Angle B =

Angle C =

The sum of the angles in a triangle is always

. Therefore, we can write the equation:

Substitute the given expressions for the angles into the equation:

Now, we need to solve this equation for x.
Combine the terms with x:

Add 13 to both sides of the equation:

Divide by 10 to find the value of x:

Now that we have the value of x, we can find the measure of angle C by substituting x into the expression for angle C:

Calculate the product

Now subtract 13 from this result:

Let’s verify by finding the measures of angles A and B as well:

Now, let’s check if the sum of the angles is

The sum is indeed

, so our calculations are correct.

The final answer is the measure of angle C.

The final answer is