Question

The vertical angle of an isosceles triangle is twice the base angles. Calculate the sizes of the angles in the triangle.

a. 30°, 60°, 90°

b. 45°, 45°, 90°

c. 60°, 60°, 60°

d. 75°, 75°, 30°

Answer 1

The angles in the isosceles triangle are 45 degrees, 45 degrees, and 90 degrees.

Step-by-step explanation:

In an isosceles triangle, the base angles are congruent (have the same measure) and the vertical angle is formed by the two congruent sides. It is given that the vertical angle is twice the measure of the base angles.

Let's assume the measure of each base angle is x. Since the vertical angle is twice the base angle, it would be 2x.

Since the sum of the angles in a triangle is 180 degrees, we can calculate the measure of the angles:

x + x + 2x = 180 degrees

4x = 180 degrees

x = 45 degrees

Therefore, the angles in the isosceles triangle are 45 degrees, 45 degrees, and 90 degrees. Answer option (b) 45°, 45°, 90° is correct.