Answer:
7: x = 23
(3x + 4) = (3(23) + 4) = 69 + 4 = 73
(5x - 8) = (5(23) - 8) = (115 - 8) = 107
8: x = 7
substitute x
(top is 59deg and bottom is 121deg) -> you can check by seeing if they add up to 180deg
9: x = 10
substitute x
(top is 80deg and bottom is 80deg)
10: x = 20
substitute x
(top is 67deg and bottom is 67deg)
Step-by-step explanation:
7: They're parallel lines cut by two transversal and since the two expression are same side interior angles, they are supplementary (they add up to 180deg)
so you do:
(3x+4) + (5x-8) = 180 you add the left side together
8x - 4 = 180 add 4 to both sides
8x = 184 divide by 8
x = 23
8: They're also supplementary angles (one easy way is know if angles are supplementary is if one is acute and one is obtuse) so it is
(7x+10) + (15x+16) = 180
22x + 26 = 180
22x = 154
x = 7
9: They're similar triangles and are located in the same angle. So, you set them equal to each other.
6x+20 = 8x
20 = 2x
x = 10
10: These are also parallel lines cut by two transversal but they're alternate interior angles. This means that they equal to each other.
3x+7 = 4x-13
3x+20 = 4x
x = 20
