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?

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