## ACT Math Tutorial

#### Intro

In this problem, given triangle ABC, you are asked to find angle B. Angles A and C are not given to you.

#### Sample Problem #### Solution

To solve this problem, you have a couple of options:

1. Recall that straight lines are 180 degrees. So angle A would be: 142 + x = 180. After solving for x in this simple equation, x= 38. Use the same process on angle C. 140 + y = 180. Solve for y, and y= 40. Now you have 2 of the 3 angles of the triangle. The sum of the measures of the triangle equals 180, so solve this final equation:
38 + 40 + z = 180, solving for z, you get z = 102. So angle B = 102 degrees.

2. Recall that the sum of the exterior angle is equal to the sum of the remote interior angles. In the case, take the 140 degree angle. The 140 degree angle would be equal to Angle B plus Angle A. We can find angle A by subtracting 142 from 180, so angle A is 38 degrees. So our equation to solve looks like this: 38 + x = 140, solving for x, gives us 102. So, Angle B equals 102 degrees.  