Question

In an isosceles triangle AABC, if ∠A measures 45 degrees, what is the measure of ∠B?

A) 45 degrees
B) 90 degrees
C) 135 degrees
D) 60 degrees

Answer 1

The measure of ∠B in an isosceles triangle ABC with ∠A measuring 45 degrees is 90 degrees, as the sum of the angles in a triangle is always 180 degrees.

Step-by-step explanation:

In an isosceles triangle, the angles opposite the two equal sides are also equal. Since ∆ABC is isosceles and ∠A measures 45 degrees, this means that ∠C also measures 45 degrees because A and C are the angles opposite the equal sides. Using the fact that the sum of the angles in a triangle equals 180 degrees, we can find the measure of ∠B by subtracting the sum of ∠A and ∠C from 180 degrees.

∠A + ∠B + ∠C = 180°

45° + ∠B + 45° = 180°

∠B + 90° = 180°

∠B = 180° - 90°

∠B = 90°

Therefore, the measure of ∠B is 90 degrees.