Question

Have no clue how to do these questions, plz help! Plz explain how u solved them as well.

Answer 1

To find x in the first problem you would make 4x and 8x-12 equal to each other because vertical angles are congruent. x would equal 3. When you plug it in, both of the angles with x equal 12.

Answer 2

1) Vertical angles are equal, so we can set 4x and 8x - 12 equal to each other. 

4x = 8x - 12

-4x = -12 (subtract 8x from both sides)

x = 3 (divide both sides by -4)

We can then substitute 3 in for x in 8x - 12.

8(3) - 12 

12

Because adjacent angles equal 180, we can put 6y + 10 and 12 (8x - 12) into an equation like this:

6y + 10 + 12 = 180

6y + 22 = 180 Combine like terms
 
6y = 158 Subtract 22 from both sides

y = 26 1/3 Divide both sides by 6

2) When two parallel lines go through another line, they form equal angles. Therefore we can set 3x equal to 48.

3x = 48 

x = 16

We can then substitute 16 in for x in 4x - 8. 

4(16) - 8 = 56

Remember, when two parallel lines go through another line, they form equal angles. So the top angle in the smaller triangle must by 56. We know the other two angles are y^2 and 48, so we can add them all equal to 180 (the degrees in a triangle). 

y^2 + 48 + 56 = 180 

y^2 + 104 = 180 Combine like terms

y^2 = 76 Subtract 104 from both sides

y = ~8.72 Take the square root of both sides