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)   (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
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)   (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
~~~~~~~~~~~~~~~~~~ 

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  = 75 degrees each.

Solved.



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