SOLUTION: The measure of the vertex angle of an isosceles triangle is 10 degrees less than thrice the measure of one of its base angles. Find the measure of the vertex angle.

Question 1200907: The measure of the vertex angle of an isosceles triangle is 10 degrees less than thrice the measure of one of its base angles. Find the measure of the vertex angle.
Found 3 solutions by Theo, greenestamps, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let B equal one of the base angles.
let V equal the vertex angle.
you get:
180 = 2A + V
V = 3A - 10
replace V in the firsts equation with 3A - 10 from the second equation to get:
180 = 2A + 3A - 10
add 10 to both sides of the equation and combine like terms to get:
190 = 5A
solve for A to get:
A = 190/5 = 38
V = 3A - 10 = 3*38 - 10 = 114 - 10 = 104
confirm by:
180 = 2 * 38 + 104 = 76 + 104 = 180
your solution is that the vertex angle is 104 degrees.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

let x be the measure of each base angle
then the measure of the vertex angle is 3x-10

The sum of the angle measures is 180:

(x)+(x)+(3x-10)=180
5x-10=180
5x=190
x=38

ANSWER: The measure of the vertex angle is 3x-10 = 3(38)-10 = 104 degrees

Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Either base angle, b
The vertex angle, 180-2b

Vertex angle is 10 degrees less than either base angle:

-

Vertex angle's measure, .

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