Question

In an isosceles triangle, a base angle is four times its vertical angle. Find all the angles of the triangle.​

Answer 1

In an isosceles triangle, the base angle is four times its vertical angle. The vertical angle measures 20 degrees, and each base angle measures 80 degrees. Therefore, the angles of the triangle are 20 degrees, 80 degrees, and 80 degrees.

Step-by-step explanation:

An isosceles triangle is a triangle with two sides of equal length and two base angles that are congruent. Let's denote the measure of the vertical angle as x degrees. Since the base angles are congruent, each base angle has a measure of 4x degrees. The sum of the angles in a triangle is always 180 degrees, so we can set up the equation:

x + 4x + 4x = 180

9x = 180

x = 20

Therefore, the measure of the vertical angle is 20 degrees, and each base angle has a measure of 4x = 4(20) = 80 degrees. So, the angles of the isosceles triangle are 20 degrees, 80 degrees, and 80 degrees.