Answer: (I worked left-right instead of column 1, then column 2. That's why the answers are jumbled up. 2 on my work corresponds to 4 in the pic, 3 corresponds to 2, 4 corresponds to 5, and 5 corresponds to 3.)
1. 75 degrees
2. 112 degrees
3. 89 degrees
4. x is 8, so 111 degrees
5. x is 3 in both cases, so 90 degrees each
6. x is -7, so 130 degrees
Step-by-step explanation:
1. Adjacent angles are the same measurement. Since the one labeled is 75 degrees, and the question marked angle is adjacent, it is also 75 degrees.
2. The angles shown are complementary, so they both equal 180 degrees. To find the angle marked with "?", subtract 68 from 180 for 112 degrees.
3. The angle labeled is 89 degrees. The one labeled with "?" should be the same, as it is below it, and on the same point as the labeled one. So, 89 degrees is the measurement.
4. The labeled angle is 69 degrees. 180 - 69 is 111 degrees. The equation shown now becomes 12x + 15 = 111. 111 - 15 is 96, which means 12x = 96. Divide both sides by 12 to get x equalling 8.
5. These lines are all perpendicular, so they're all 90 degrees. 29x + 3 = 90, and 31x - 3 = 90 are the new equations. I will attempt x as 3, to see if it's a true value. 29(3) is 87, and 87 + 3 is 90, so 3 is true there. 31(3) is 93, and 93 - 3 is also 90. So x is 3 in both cases
6. We already know one of the angles is 50 degrees. These are complementary, so subtract 50 from 180 to get 130 degrees. So, the equation is x + 137 = 130, which then becomes, 137 + -x = 130. 137 minus 30 is 7, so x is -7.
