Question

An isosceles, obtuse triangle has one angle with a degree measure that is 50$\%$ larger than the measure of a right angle. What is the measure, in degrees, of one of the two smallest angles in the triangle? Express your answer as a decimal to the nearest tenth.

Answer 1

Answer: 22.5°

Each of the two smallest angles in the triangle are 22.5°

Explanation:

Isosceles triangle is a triangle with two equal sides and two equal angles

The largest angle is 50% more than right angle

Let L represent the largest angle

L = 150% of 90°

L = 1.5 × 90°

L = 135°

The other two angles are equal and can be represented by x

Sum of angles in a triangle is 180°

L + x + x = 180°

2x = 180 - L

x = (180 - 135)/2

x = 45/2

x = 22.5°