Question

A triangle has angle measures that are related as follows:

• The largest angle is eight times the smallest angle.


• The middle angle is triple the smallest angle..


a) write an equation to model the relationship


b) solve the equation and then determine the measure of each angle. Sketch the triangle and label the angle measures.

Answer 1

a) a +8a +3a = 180°

b) 15°, 45°, 120°

c) see attached

Explanation:

a)

Let 'a' represent the measure of the smallest angle. The largest angle is 8a, and the middle angle is 3a. The sum of angles, as always, is 180°.

a +8a +3a = 180° . . . . . . equation modeling the relationship

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b)

12a = 180° . . . . . . collect terms

a = 15° . . . . . . . divide by 12

3a = 3×15° = 45°

8a = 8×15° = 120°

The angle measures are 15°, 45°, and 120°.

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c)

see attached. We have arbitrarily let the shortest side be 10 units.