Question

Two angles of a triangle

have the same measure.
The sum of the measures
of these angles is one-half
the measure of the third
angle. Find the measures
of the angles of the
triangle.

Answer 1

The measures of the angles are 45 degrees, 90 degrees, and 45 degrees.

Step-by-step explanation:

To find the measures of the angles of the triangle, let's denote the measures of the two angles that are equal as x. The measure of the third angle will be 2x since the sum of the measures of the first two angles is half of the measure of the third angle.

Since the sum of the measures of the angles of a triangle is 180 degrees, we can write the equation: x + x + 2x = 180. Simplifying, we get: 4x = 180, x = 45.

Therefore, the measures of the angles are: x = 45 degrees, 2x = 90 degrees, and x = 45 degrees.