One angle of a triangle measures 10 degrees more than the second. The measure of the third angle is

twice the sum of the measures of the first two angles. Find the measure of each angle. [Hint: the sum of

the three angles in a triangle equals 180°.]

Answer:first angle = 25 degrees

Second angle = 35 degrees

Third side = 120/degrees

Step-by-step explanation:

Let the size of the second angle be x degrees.

One angle of a triangle measures 10 degrees more than the second. This means that the size of the first angle is (x + 10) degrees.

The measure of the third angle is

twice the sum of the measures of the first two angles. This means that

The third angle = 2 (first angle + second angle). So the size of each angle is

First angle (x + 10) degrees

Second angle = x degrees

Third angle = 2 (x + 10 + x) =

(4x + 20) degrees

Sum of angles in a triangle = 180

degrees. Therefore,

x + 10 + x + 4x + 20 = 180 degrees

6x + 30 = 180

6x = 180 - 30 = 150

x = 150/6 = 25 degrees

First angle = x + 10 = 25 + 10 = 35

Third angle = 4x + 20 = 4 * 25 + 20

= 100 + 20 = 120 degrees