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
