SOLUTION: In an isosceles triangle, two of the angles are equal in measure. If the third angle is 21° less than three times the other angles, find the measure of all three angles.

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Question 583072: In an isosceles triangle, two of the angles are equal in measure. If the third angle is 21° less than three times the other angles, find the measure of all three angles.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
In an isosceles triangle, two of the angles are equal in measure. If the third angle is 21° less than three times the other angles, find the measure of all three angles.
Oh oh!  There are two things you could mean by the words:

         "three times the other angles"

You could mean

1. "three times the measure of either one the other two angles"

or

2. "three times the sum of the measures of the other two angles"

If you mean this:

In an isosceles triangle, two of the angles are equal in measure. If the third angle is 21° less than three times THE MEASURE OF EITHER ONE OF the other TWO angles, find the measure of all three angles.
Then if each of the base angles has measure x, then since the 3rd angle's
measure is:

"21° less than three times the mwasure of either one of the other two angles
 
then the third angle = 3x-21°

Then we use the fact that the sum of all three angles of any triangle is 180°.
So the equation is

x + x + (3x-21) = 180

Simplify and solve that and get x = 40.2° for each of the base angles, 
The third angle is 3x-21° = 3(40.2°) - 21° = 99.6°

So the triangle drawn to scale looks like this:

  

However if you meant this:

In an isosceles triangle, two of the angles are equal in measure. If the third angle is 21° less than three times THE SUM OF THE MEASURES OF the other TWO angles, find the measure of all three angles.
Then if each of the base angles has measure x, then since the 3rd angle's
measure is:

"21° less that three times the sum of the measure of either one of the other
two angles, 

the third angle = 3(x+x)-21° = 3(2x)-21° = 6x-21°

Then we use the fact that the sum of all three angles of any triangle is 180°.
So the equation is

x + x + (6x-21) = 180

Simplify and solve that and get x = 25.125° for each of the base angles, 
The third angle is 6x-21° = 6(25.125°) - 21° = 129.75°

So the triangle drawn to scale looks like this:

  

Edwin