Use the Triangle Angle Sum Theorem to find the measure of the largest angle of a triangle with angle measures 3x + 10, 2x - 3, and 5x

Answer 1

The measure of the largest angle of a triangle is found by adding the measures of all three angles and setting it equal to 180 degrees.

(3x + 10) + (2x - 3) + (5x) = 180

Combining like terms:
10x + 7 = 180

Subtracting 7 from both sides:
10x = 173

Dividing both sides by 10:
x = 17.3

Now we can plug this value back into any of the angle measures to find the measure of the largest angle. Let's use the first angle measure:

3x + 10 = 3(17.3) + 10 = 51.9 + 10 = 61.9

So, the measure of the largest angle in the triangle is 61.9 degrees.