SOLUTION: How do you solve this? In an isosceles triangle, each base angle has a measure which is 30 more than four times the measure of the vertex angle. Find the measure of a base angle.

Algebra ->  Triangles -> SOLUTION: How do you solve this? In an isosceles triangle, each base angle has a measure which is 30 more than four times the measure of the vertex angle. Find the measure of a base angle.       Log On


   

Question 764258: How do you solve this?
In an isosceles triangle, each base angle has a measure which is 30 more than four times the measure of the vertex angle. Find the measure of a base angle.
Found 2 solutions by ramkikk66, Cromlix:
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!

Remember that the sum of the 3 angles in any triangle is 180.

In an isosceles triangle, both the base angles are equal. 

Let the measure of the vertex angle be x.

Then the measure of each base angle = 4*x + 30.

Sum of the 3 angles = 2(4*x + 30) + x = 180

8%2Ax+%2B+60+%2B+x+=+180

9%2Ax+=+120

x+=+40%2F3

Measure of each base angle = 4%2A40%2F3+%2B+30+=+160%2F3+%2B+30+=+250%2F3


:)



Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Vertex angle = x
Base angle = 30 + 4x
Total of 180 degrees in a triangle.
2(30 + 4x) + x = 180
60 + 8x + x = 180
60 + 9x = 180
9x = 180 - 60
9x = 120
x = 120/9
x = 13.3 degrees
Base angle = 83.3 degrees.
Hope this helps.
:-)