Isoceles Triangle has base angles twice size of third angle

[jramirez23]

All triangles add up to 180 degrees. In isoceles triangle ABC, each of the 2 base angles is twice as large as the third angle. What are the measure of the three angles of the triangle?

I am extremely perplexed, I don't even know where to start except I know that isoceles triangles have two angles that are equal in length and that all angles must add up to 180 degrees.

 

[stapel]

All triangles add up to 180 degrees. In isoceles triangle ABC, each of the 2 base angles is twice as large as the third angle. What are the measure of the three angles of the triangle?

Whatever is the size of the third angle, the first and second (equal) angles have twice the size. If the third angle is one "part" of the angle sum, then how many parts is each of the equal angles?

Then how many total parts are there?

Since the total of these parts is 180, how much is each part?

One part is the size of the third angle. Two parts is the size of the other angles. How much does each of the other angles then measure?

Eliz.

 

[pka]

If x is the measure of the vertex angle the we have,
\(\displaystyle 2x + 2x + x = 180\).
Solve for x.

 

[jramirez23]

Re:

All triangles add up to 180 degrees. In isoceles triangle ABC, each of the 2 base angles is twice as large as the third angle. What are the measure of the three angles of the triangle?

Whatever is the size of the third angle, the first and second (equal) angles have twice the size. If the third angle is one "part" of the angle sum, then how many parts is each of the equal angles?

Then how many total parts are there?

Since the total of these parts is 180, how much is each part?

One part is the size of the third angle. Two parts is the size of the other angles. How much does each of the other angles then measure?

Eliz.

The answer I got was 72 for two angles, and 36 for one angle. Am I correct?

 

[stapel]

The answer I got was 72 for two angles, and 36 for one angle. Am I correct?

The answer to any "solving" problem can be checked by plugging it back into the original exercise, and verifying that it works. :idea:

In this case: Is 36 half of 72? Does 72 + 72 + 36 equal 180? :wink:

Eliz.