SOLUTION: In an isosceles triangle,the measure of one base angle is 15 degrees more than twice the measure of the vertex angle. Find the measures of all three angles

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Question 1207174: In an isosceles triangle,the measure of one base angle is 15 degrees more than twice the measure of the vertex angle. Find the measures of all three angles
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
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In an isosceles triangle,the measure of one base angle is 15 degrees more than twice the measure of the vertex angle. Find the measures of all three angles
Let vertex angle be x deg
Base angles= (2x+15) deg ( base angles are equal in isoscles triangle)
x+(2x+15)+(2x+15) = 180 ( sum of angles of triangle)
5x+30 =180
5x = 180-30
5x =150
x=30
Vertex = 30 deg
Base angles = (2x+15)
Plug x
Base angles = 2*30+15= 75
Vertex angle: 30 degrees
Base angles: 75 degrees

Check
75+75+30 =180



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
In an isosceles triangle, the measure of one base angle is 15 degrees more
than twice the measure of the vertex angle. Find the measures of all three angles
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Let x be the measure of the vertex angle, in degrees.

Then the angles at the base are (2x+15) degrees each; they are congruent.


The sum of angles is 180 degrees

    (2x+15) + (2x+15) + x = 180

     5x + 30 = 180

     5x = 180 - 30 = 150

     5x = 150

      x = 150/5 = 30.


ANSWER.  The vertex angle is 30 degrees.  The angles at the base are %28180-30%29%2F2 = 75 degrees each.

Solved.