Question

Each of the equal angles of an isosceles triangle is four times as large as the third angle. What is the measure of each angle?

Answer 1

In an isosceles triangle where each of the equal angles is four times the third angle, the measures are 80 degrees for each of the equal angles and 20 degrees for the third angle.

Step-by-step explanation:

To solve the problem involving an isosceles triangle where each of the equal angles is four times as large as the third angle, we start by recognizing that the sum of all angles in a triangle is 180 degrees. Let's call the third angle x. Therefore, each of the larger equal angles would be 4x, resulting in two angles of 4x each. We then set up the equation:

4x + 4x + x = 180

This simplifies to:

9x = 180

And, when we solve for x:

x = 180 / 9

x = 20 degrees

Thus, the measure of each of the larger equal angles is:

4x = 4 * 20

4x = 80 degrees

So, the third angle is 20 degrees, and each of the equal angles is 80 degrees.