Let’s solve each problem step by step. Remember:
-
Complementary angles add up to
90°.
-
Supplementary angles add up to
180°.
We’ll go one by one.
---
Problem 1:
Angle shown: 60°, and it’s part of a right angle (90° total).
So, x + 60 = 90
→ x = 90 - 60 =
30
✔ Check: 30 + 60 = 90 → correct.
---
Problem 2:
Angle shown: 57°, and it’s part of a right angle (90° total).
So, x + 57 = 90
→ x = 90 - 57 =
33
✔ Check: 33 + 57 = 90 → correct.
---
Problem 3:
Angles on a straight line: 45° and x. Straight line = 180°.
So, x + 45 = 180
→ x = 180 - 45 =
135
✔ Check: 135 + 45 = 180 → correct.
---
Problem 4:
Two angles on a straight line: x and 12°.
So, x + 12 = 180
→ x = 180 - 12 =
168
✔ Check: 168 + 12 = 180 → correct.
---
Problem 5:
Three angles on a straight line: (x - 1)°, 117°, and another angle? Wait — looking at the diagram description: it shows two rays forming three angles on a straight line? Actually, from standard problems like this, if there are two labeled angles on a straight line, they should sum to 180. But here it says “(x - 1)°” and “117°”, and they appear to be adjacent on a straight line.
Wait — actually, rechecking: in many such worksheets, when you see two angles on a straight line with labels, they are supplementary. So likely:
(x - 1) + 117 = 180
→ x - 1 = 180 - 117 = 63
→ x = 63 + 1 =
64
✔ Check: (64 - 1) + 117 = 63 + 117 = 180 → correct.
---
Problem 6:
Right angle split into two parts: x° and 44°.
So, x + 44 = 90
→ x = 90 - 44 =
46
✔ Check: 46 + 44 = 90 → correct.
---
Problem 7:
Right angle split into two parts: x° and 8°.
So, x + 8 = 90
→ x = 90 - 8 =
82
✔ Check: 82 + 8 = 90 → correct.
---
Problem 8:
Straight line with two angles: 105° and x°.
So, x + 105 = 180
→ x = 180 - 105 =
75
✔ Check: 75 + 105 = 180 → correct.
---
All answers verified.
Final Answer:
1. 30
2. 33
3. 135
4. 168
5. 64
6. 46
7. 82
8. 75
Parent Tip: Review the logic above to help your child master the concept of complementary and supplementary angle worksheet.
