In a​ triangle, the measure of the first angle is twicetwice the measure of the second angle.

Question

In a triangle, the measure of the first angle is twice twice the measure of the second angle. The measure of the third angle is 96 degree° 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 degrees° to find the measure of each angle?

 

Answer 1

Okay, so let the 2nd angle be just x.  Then the first angle is 2x, since it is twice the measure of the second angle (2 times x), and the 3rd angle is 96 + x, since it is 96 MORE (addition) than the 2nd angle.  So our 3 angles are:

 

Angle 1: 2x

Angle 2: x

Angle 3: 96 + x

 

We know that all 3 angles in a triangle add up to be 180.  So we can add these 3 angles together and set it equal to 180. 

 

2x + x + (96 + x) = 180

3x + 96 + x = 180

4x + 96 = 180

4x = 84

x = 21

 

Now we can plug x = 21 back into our 3 angles from earlier getting:

 

Angle 1: 2(21) = 42

Angle 2: 21

Angle 3: 96 + 21 = 117

 

If you add all 3 of these up, you'll see that they equal 180.