Question

In an isosceles triangle, the measure of the vertex angle is 4x+ 6. The measure of each base angle is (10x - 6). What is the actual measure of the vertex angle?

Answer 1

vertex angle = 37°

Explanation:

the base angles of an isosceles triangle are congruent (equal )

the sum of the 3 angles in the triangle is 180°

sum the 3 angles, equate to 180 and solve for x

4x + 6 + 10x - 6 + 10x - 6 = 180 ( simplify left side )

24x - 6 = 180 ( add 6 to both sides )

24x = 186 ( divide both sides by 24 )

x = 7.75

Then

vertex angle = 4x + 6 = 4(7.75) + 6 = 31 + 6 = 37°