Answer:
1. x = 23
2. y = 14
3. n = 17.5
4. x = 12
5. n = 11
Step-by-step explanation:
Complementary angles are equal to 90°
Vertical angles are congruent, which means they are equal to each other.
Supplementary angles are equal to 180°
1.
2x - 3 + 47 = 90
Step 1: Combine like terms (-3 + 47)
2x (-3 + 47) = 90
2x + 44 = 90
Step 2: Subtract 44 from both sides
2x + 44 - 44 = 90 - 44
2x = 46
Step 3: Divide by 2 on both sides
2x/2 = 46/2
Step 4: Simplify
x = 23
2.
5y + 12 = 82
Step 1: Subtract 12 from both sides
5y + 12 - 12 = 82 - 12
5y = 70
Step 2: Divide by 5 on both sides
5y/5 = 70/5
Step 3: Simplify
y = 14
3.
4n - 5 + 115 = 180
Step 1: Combine like terms (-5 + 115)
4n (-5 + 115) = 180
4n + 110 = 180
Step 2: Subtract 110 from both sides
4n + 110 - 110 = 180 - 110
4n = 70
Step 3: Divide by 4 on both sides
4n/n = 70/4
Step 4: Simplify
n = 17.5
4.
Since m∠XYZ = 110°
3x + 2 + 72 = 110
Step 1: Combine like terms (2 + 72)
3x + (2 + 72) = 110
3x + 74 = 110
Step 2: Subtract 74 from both sides
3x + 74 - 74 = 110 - 74
3x = 36
Step 3: Divide by 3 on both sides
3x/3 = 36/3
Step 4: Simplify
x = 12
5.
5n + 35 = 90
Step 1: Subtract 35 from both sides
5n + 35 - 35 = 90 - 35
5n = 55
Step 2: Divide by 5 on both sides
5n/5 = 55/5
Step 3: Simplify
n = 11
