Question

In a triangle , the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 80 more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180 to find the measure of each angle .

Answer 1

25, 50, and 105.

Explanation:

Let the first angle be A, the second angle be B, and the third angle be C.

First, the sum of the three angles in a triangle is 180. Thus:

`A+B+C=180`

We know that the measure of A is twice the measure of B. Thus:

`A=2B`

And the measure of C is 80 more than the measure of B. So:

`C=80+B`

Let's substitute A and C into the original equation:

`2B+B+80+B=180`

Now, let's solve for the second angle (B). Combine like terms:

`4B+80=180`

Subtract 80 from both sides:

`4B=100`

Divide both sides by 4:

`B=25`

So, the second angle is 25 degrees.

This means that the first angle is 2(25) or 50 degrees.

And the third angle is 80+25 or 105 degrees.

And we're done!

The angles are 25, 50, and 105.