```Question 624625
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Hi, there--

The Problem:
In a triangle, the measure of the first angle is 15 degrees more than twice the measure of the
second angle. the measure of the third angle exceeds that of the second angle by 25 degrees.
What is the measure of each angle?

Solution:
Let a be the measure of the first angle.
Let b be the measure of the second angle.
Let c be the measure of the third angle.

Now we need to write three equations using information inform the problem statement.
We know that, "the measure of the first angle is 15 degrees more than twice the measure of the
second angle." So,
[the measure of the first angle] = [15 degrees] + [twice the measure of the second angle]

An equation representing this relationship is
a =15+2b

We also know that, "the measure of the third angle exceeds that of the second angle by
25 degrees." So,
[the measure of the third angle] = [25 degrees] + [the measure of the second angle]

An equation representing this relationship is
c=25+b

A math fact that will help us here: the sum of the interior angles in a triangle is always
180 degrees. We can write this relationship as an equation,
a+b+c=180

Now we have three equations in three variables. We will use the substitution method to solve
for a, b, and c.

We see in the 1st equation that a is equivalent to 15+2b. We see in the 2nd equation that c is
equivalent to 25+b. Make these substitutions in the third equation.
a+b+c=180
(15+2b) + b + (25+b) = 180

Solve for b by combining like terms. 2b+b+b is 4b and 15+25 is 40
4b+40=180

Subtract 40 from both sides of the equation.
4b+40-40=180-40
4b=140

Divide both sides of the equation by 4. 4b/4 is b and 140/4 is 35.
b=35

In the context of this problem, the equation b=35 means that the measure of the second angle is
35 degrees.

Substitute 35 for b in the first and second equations.
a=15+2b
a=15+2(35)
a=15+70
a=85
The measure of the first angle is 85 degrees.

c=25+b
c=25+35
c=60
The measure of the third angle is 60 degrees.

The measures of a, b, and c are 85, 35, and 60 degrees, respectively.

We need to make sure that these angle measure add up to 180 degrees.
85+35+60=180 True!

That's it. Please email me if you have questions or comments about the solution. I'm happy to
explain in more detail, and I'd appreciate your feedback.

Ms.Figgy
math.in.the.vortex@gmail.com
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