The measure of the angles of a triangle are in the extended ratio 2:8:10. What is the measure of the largest angle?

Question

A. 9
B. 18
C. 90
D. 72

Answer 1

To find the measure of the largest angle in the triangle, we need to first determine the sum of all three angles.

Let the three angles be 2x, 8x, and 10x.
According to the extended ratio, the sum of all three angles is 2x + 8x + 10x = 20x.

Since the sum of the angles in a triangle is 180 degrees, we can write:
20x = 180
x = 9

Therefore, the largest angle is 10x = 10 * 9 = 90 degrees.

So, the correct answer is:

C. 90