Question

How do you find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles?

Answer 1

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 =2b-40`

The sum of the measures of the angles of a triangle is 180.
`b+b+v=180`

Substitute `2b-40` for `v`.
`b+b+2b-40=180`
`4b-40=180` `color(white)(aaaaa)`Combine like terms.
`color(white)(aa)+40color(white)(a)+40` `color(white)(aaaaa)`Add 40 to both sides.

`4b=220`

Divide by 4
`(4b)/4=220/4`
`b=55`

`v=2b-40`
`v=2(55)-40=70`