Question

What is the sum of the angles in a triangle where the largest angle is 20 degrees more than the smallest angle, and the third angle is 10 degrees more than the smallest angle? A) 150 degrees B) 160 degrees C) 170 degrees D) 180 degrees

Answer 1

The sum of the interior angles of any triangle is always 180 degrees.

In this problem, we have a triangle with three angles where the largest angle is 20 degrees more than the smallest angle, and the third angle is 10 degrees more than the smallest angle.

Let's denote the smallest angle as x. Therefore, the largest angle is x + 20 and the third angle is x + 10.

Adding all angles of the triangle together will give us the equation:

x (the smallest angle) + x + 20 (the largest angle) + x + 10 (the third angle) = 180

This simplifies to 3x + 30 = 180. To solve for x, we would first subtract 30 from both sides of the equation, getting:

3x = 150.

Then divide by 3 to isolate x, getting:

x = 50

If we then add the three angles together using x as the smallest angle:

50 (smallest angle) + 70 (largest angle) + 60 (third angle) = 180 degrees

So, the answer is D) 180 degrees.