Question

The first angle of a triangle measures 10° more than the second angle and the third angle measures 10° more than the first angle how many degrees are in each angle

Answer 1

The second angle measures 50 degrees, the first angle measures 60 degrees, and the third angle measures 70 degrees.

Step-by-step explanation:

Let's represent the second angle as x degrees. Since the first angle measures 10° more than the second angle, it can be represented as (x + 10) degrees. Similarly, the third angle measures 10° more than the first angle, so it can be represented as ((x + 10) + 10) degrees, which simplifies to (x + 20) degrees.

By the triangle angle sum theorem, the sum of the three angles in a triangle is always 180 degrees. Therefore, we can write the equation:

(x) + (x + 10) + (x + 20) = 180

Simplifying, we have:

3x + 30 = 180

Subtracting 30 from both sides, we get:

3x = 150

Dividing both sides by 3, we find:

x = 50

Therefore, the second angle measures 50 degrees, the first angle measures (50 + 10) = 60 degrees, and the third angle measures (50 + 20) = 70 degrees.

Learn more about Triangle angles