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

Answer:

The measure of the first angle is 50°.

Step-by-step 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°.)