Complementary angles are two angles which sum is equal to 90 degrees
angle DFG and angle JKL are complementary angles
DFG = x + 3
JKL = x - 5
x-5 +x + 3 = 90
Add like terms
2x - 2 = 90
Add 2 to each side
2x = 92
Divide each side by 2
x = 46
Let's plug 46 into x for angle DFG
46 + 3 = 49
Since they add up to 90, we can subtract 49 from 90 to get angle JKL
90 - 49 = 41
DFG = 49
JKL = 41
For question 5, bisecting means cutting something in half. Angles LMO and NMO are equal to each other.
6x - 21 = 2x + 31
Let's subtract 2x from both sides and add 21 to both sides
4x = 52
Divide each side by 4
x = 13
Let's plug 13 in for x
LMO = 6(13) - 21 = 57
Since LMO and NMO are equal, we can multiply 57 by 2
57 * 2 = 114
The measure of LMN is 114