Question

A landscaper is forming an isosceles triangle in a flowerbed using chrysanthemums. She wants m∠A to be three times the measure of ∠B and ∠C. What should the measure of each angle be?

Solution

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We let mB=mC=xm\angle B=m\angle C=x so that mA=3xm\angle A=3x.

By Triangle Angle-Sum Theorem, the sum of the measures of the angles of a triangle is 180 so we can write:

mA+mB+mC=180m\angle A + m\angle B+ m\angle C=180

3x+x+x=1803x+x+x=180

5x=1805x =180

Divide both sides by 5:

x=36x=36

Hence,

mA=108°\color{#c34632}{m\angle A= 108\text{\textdegree}}

mB=36°\color{#c34632}{m\angle B=36\text{\textdegree}}

mC=36°\color{#c34632}{m\angle C=36\text{\textdegree}}

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