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. what is the measure of the first angle?​

Answer 1

The measure of the first angle is 50°.

Explanation:

Let the three angles be a, b, and c.

The measure of the first angle is twice the measure of the second angle. In other words:

`a=2b`

The measure of the third angle is 80° more than the measure of the second angle. In other words:

`c=b+80`

And since the interior angles of a triangle must equal 180°:

`a+b+c=180`

Substitute a and c:

`(2b)+b+(b+80)=180`

Combine like terms:

`4b+80=180`

Subtract 80 from both sides:

`4b=100`

And divide both sides by four:

`b=25^\circ`

So, the measure of the second angle is 25°.

Since the measure of the first is twice the second, the measure of the first angle is 50°.

(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)