Hi, there--
THE PROBLEM:
The sum of three times an angle and twice its complement is 215. Find the measures of the
angles.
A SOLUTION:
First, we define a variable:
Let m be the measure of the first angle.
We also need this definition:
"Two angles whose measures sum to 90 degrees are said to be COMPLEMENTARY."
Write an expression for the measure of the second angle. Since the measures of the two
angles must add up to 90 degrees, the measure of the second angle is 90-a.
(Note: a + 90-a = 90)
Now we translate the problem statement from English into an equation. Let's do this in steps.
"Three times an angle" means three times the measure of the first angle." We defined the
measure of the angle as a. Three times a is 3a.
"Twice the complement" means two times the measure of the second angle. The measure of
the second angle is 90-a. Two times 90-a is 2(90-a).
These two expressions added together equal 215.
3a + 2(90-a) = 215.
Now we solve for a. Use the distributive property to clear the parentheses.
3a + 180 - 2a = 215
Combine like terms. (3a-2a=a)
a + 180 = 215
Subtract 180 from both sides to isolate the variable on the left. (180-180=0)
a + 180 - 180 = 215 - 180
a = 35
In the context of this problem, a=35 means the measure of the first angle is 35 degrees.
Since the the two angles are complementary, the sum of their measure is 90 degrees. Thus
the measure o the second angle is 90-35=55 degrees.
Let's check these angle measures in the original problem statement:
"The sum of three times an angle and twice its complement is 215."
The sum of [three times 35] and [twice 55] is 215.
The sum of [105] and [110] is 215.
105 + 110 = 215
TRUE
The measures of the two angles are 35 degrees and 55 degrees.
Hope this helps,
Mrs. Figgy
math.in.the.vortex@gmail.com
