Question

What is the measure of a base angle of an isosceles triangle if the measure of the vertex tangle is 38 degrees and the two congruent sides each measure 21 units?

Answer 1

Each base angle of an isosceles triangle in this problem measures 71 degrees, calculated by subtracting the vertex angle from 180º and dividing the result by 2.

Step-by-step explanation:

The measure of a base angle of an isosceles triangle is determined by subtracting the measure of the vertex angle from the total sum of the triangle's angles, which is 180 degrees, and then dividing the remaining sum by 2, since the base angles are congruent (equal). Given that the vertex angle is 38 degrees, we subtract this from 180 degrees to obtain the sum of the measures of the two base angles.

Step-by-step process:

1. Sum of angles in a triangle is 180 degrees: 180° - 38° = 142°.
2. Since the two base angles are congruent, divide the sum of the base angles by 2: 142° ÷ 2 = 71°.

Therefore, each base angle measures 71 degrees.

Answer 2

The measures of the angles of the isosceles triangle are 55, 55 and 70.

Explanation:

An isosceles triangle has two congruent base angles and a vertex angle.

Let b =the measure of one of the base angles.

Let v = the measure of the the vertex angle.

The vertex angle is 40 degrees less than the sum of the base angles.

v = b + b − 40 = 2 b − 40

The sum of the measures of the angles of a triangle is 180.

b + b + v = 180

Substitute 2 b − 40 for v .

b + b + 2 b − 40 = 180

4 b − 40 = 180

+40+40

Combine like terms.

Add 40 to both sides.

4b=220

Divide by 4

4 b/4 = 220 /4

b = 55

v = 2 b − 40

v = 2 ( 55 ) − 40 = 70