In a triangle ABC, the measure of angle A is fifteen less than twice the measure of angle B. The measure of angle C equals the sum of the measures of angle A and angle B. What is the measure of angle B?
2 Answers
If the reference to "fifteen" means
then
If the refrence to "fifteen" means
then
Explanation:
We are told explicitly that
[1]
[2]
and, implicitly (assuming the triangle lies in a Cartesian plane)
[3]
Arranging these into standard form:
[4]
[5]
[6]
Adding [5] and [6]
[7]
Multiplying [4] by 2
[8]
Subtracting [8] from [7]
[9]
Dividing by 6
[10]
Explanation:
First of all, let's translate this problem into mathematical language. I suppose that we are working with degree measures of angles (so that writing "fifteen" you meant "fifteen degrees").
We also have to "decode" another crucial information: these are angles in a triangle, so their sum equals
We want to find the measure of the angle
The measure of the angle
So dividing both sides by
Now we substitute this last result in the first equation:
and we get an equation where
Let's solve this:
Note: The only angle left is