Question

In a​ triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 70 degrees 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 degrees to find the measure of each angle.

The measure of the first angle is _____

Answer 1

66

Explanation:

x is the second angle

3x is the first angle

x+70 is the third angle

x+3x+x+70=180

5x = 110

x= 22

first angle: 3x = 3*22 = 66

Answer 2

Second angle: 22°

And the other angles are:

First angle: 66°

Third angle: 92°

Explanation:

Let be:

`x` the measure of the second angle.

`3x` the measure of the first angle.

`(x+70)`: the measure of the third angle.

Then, knowing that the sum of the interior angles of a triangle is 180 degrees, you can write this expression and solve for "x",to calculate the measure of the second angle:

`x+3x+(x+70)=180\\5x+70=180\\5x=180-70\\\\x=(110)/(5)\\\\x=22\°`

You can also know that:

First angle:

`3x=2(22\°)=66\°`

Third angle:

`x+70\°=22\°+70\°=92\°`