Problem 4
Answer: 103 degrees
Angle 1 and angle 3 are congruent angles (aka they are the same measure). This happens due to the fact that line x is parallel to line y, and because the two angles mentioned are corresponding angles.
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Problem 5
Answer: 62 degrees
Subtract the measure of angle 1 from 180 and we get: 180 - 118 = 62. I'm using the fact that the same side exterior angles are supplementary, meaning they add to 180 degrees (angle1+angle4 = 118+62 = 180). Like with problem 4, this only works if line x is parallel to line y.
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Problem 6
Answer: y = 5; each angle is 20 degrees
The two angles are congruent as they are vertical angles. Set the expressions equal to each other and solve for y
-2y+30 = 4y
30 = 4y+2y
30 = 6y
6y = 30
y = 30/6
y = 5
Now use this value of y to find the measure of each angle
4y = 4*5 = 20
-2y+30 = -2*5+30 = -10+30 = 20
as expected, each angle is the same measure (20 degrees each).
