Question

A triangle has one angle that is three times the size of another, and a third angle that is 16degrees smaller than the larger of the previous two angles. What is the measure of each angle?

Answer 1

The answers are 26 68 84

Answer 2

26, 68 and 84

Explanation:

Let the angle that is three times smaller than another be X.

Since the angle sum of a triangle is 180 degrees, we can form the following equation:

X + 3X + (3X- 16) = 180

Now we can simplify this equation:

7X - 16 = 180

7X = 196 (add 16 to both sides)

X = 196/7

X = 28

Therefore, the smallest angle is 28 degrees.

And from here we can figure out the other angles as they are 3x28 and 3x28 - 16.

So the three angles are 28 degrees, (3x28-16) 68 degrees, and (3x28) 84 degrees.