Find the angle of a triangle...

Question

The second angle of a triangle is 5 degree more than three times the first, and the third is 10 degree less than the first. Find the measure of the second angle. 

I need help...I just don't understand this problem. 

 

Answer 1

The sum of the angles of a triangle = 180

 

X is first angle

 

3X + 5 is second angle 

 

X - 10 is third angle

 

So:

 

X + 3X + 5 + X - 10 = 180

 

                    5X - 5 = 180

 

                         5X = 185

 

                           X = 37

 

first angle is 37

 

second angle is 116

 

third angle is 27

Answer 2

We have a triangle (3 sided figure with 3 angles). Let X = angle #1, Y = angle #2, Z = angle #3. From information given: 

Y = 3 X + 5 and Z = X - 10. Than, we know that sum of angles of triangle is 180, Thus, X + Y + Z = 180.

Now, substitute the defined values of Y and Z given, into the 3rd equation to get:

X + (3 X + 5) + (X - 10) = 180, then X + 3X + 5 + X - 10 = 180, then 5X - 5 = 180, then 5X = 185, so X = 37. Now, Y 3X + 5, or 3(37) + 5, or 111 + 5, or 116 degrees. Then Z = X - 10, or 37 - 10, or 27 degrees. Check: 37 + 116 + 27 + 180.