The sum of the measures of three angles in a triangle is 180 degrees. The measure of one angle of a triangle is one degree more than three times the measure of the smallest angle. The measure of the third angle is 13 degrees less than twice the measure of the second angle. Find the measure of each angle. (now the back of the book says the answers are 19 degree, 58 degree, & 103 degree) but I don't know how they got them.

19, 58 and 103

Step-by-step explanation:

Okay. Here we need to convert whatever statements we have into a mathematical expression.

Firstly, let's give the smallest angle a value of x. Where do we now go from here? The measure of one angle is 1 degree greater than 3 times the size of the smallest angle. This means the value of the second angle is 3x + 1

Now for the third angle, the question stated that the third angle is thirteen degrees less than twice the measure of the second angle. The value for this is: 2 (3x + 1) - 13

Now when we add all these angles, surely, we get a result equal to 180.

x + 3x + 1 + 2 (3x + 1) - 13 = 180

4x + 1 + 6x + 2 - 13 = 180

10x - 10 = 180

10x = 190 and x = 19.

Now the measure of the other angles are as follows:

3x + 1 = 3 (19) + 1 = 57 + 1 = 58

2 (3x + 1) - 13 = 2 (58) - 13 = 103