Question

Could you guys help me with my homework ?

Answer 1

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.

=================================================

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.

=================================================

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).