Question

Question

The angles in
triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times
as large as the smallest angle. Find the measures of all three angles.

Answer 1

9514 1404 393

Answer:

20°, 120°, 40°

Explanation:

Let s represent the smallest angle. Then the largest is (100+s) and the third angle is (2s). The sum of angles in a triangle is 180 degrees, so we have ...

s + (100+s) +(2s) = 180

4s = 80 . . . . . . . . . . subtract 100

s = 20 . . . the smallest angle

100+s = 120 . . . the largest angle

2s = 40 . . . the third angle

The angle measures are 20°, 120°, and 40°.