Let's solve the problem step by step.
🔷 Understanding Complementary Angles
Two angles are
complementary if their measures add up to
90 degrees.
So, if one angle is given, the other complementary angle can be found using:
>
Complementary Angle = 90° − Given Angle
We’ll apply this formula to each part of the worksheet.
---
✔ Solving Each Part
#### a. ∠ABC = ?
Given: One angle is
37°, and it forms a right angle (90°) with ∠ABC.
So:
> ∠ABC = 90° − 37° =
53°
✔ Answer: 53°
---
#### b. ∠PNO = ?
Given: One angle is
28°, and they form a right angle.
> ∠PNO = 90° − 28° =
62°
✔ Answer: 62°
---
#### c. ∠LJK = ?
Given: One angle is
52°
> ∠LJK = 90° − 52° =
38°
✔ Answer: 38°
---
#### d. ∠NMP = ?
Given: One angle is
46°
> ∠NMP = 90° − 46° =
44°
✔ Answer: 44°
---
#### e. ∠PRS = ?
Given: One angle is
70°
> ∠PRS = 90° − 70° =
20°
✔ Answer: 20°
---
#### f. ∠VWU = ?
Given: One angle is
54°
> ∠VWU = 90° − 54° =
36°
✔ Answer: 36°
---
#### g. ∠KLT = ?
Given: One angle is
15°
> ∠KLT = 90° − 15° =
75°
✔ Answer: 75°
---
#### h. ∠RQS = ?
Given: One angle is
60°
> ∠RQS = 90° − 60° =
30°
✔ Answer: 30°
---
#### i. ∠DCE = ?
Given: One angle is
23°
> ∠DCE = 90° − 23° =
67°
✔ Answer: 67°
---
#### j. ∠CDA = ?
Given: One angle is
18°
> ∠CDA = 90° − 18° =
72°
✔ Answer: 72°
---
#### k. ∠EFG = ?
Given: One angle is
31°
> ∠EFG = 90° − 31° =
59°
✔ Answer: 59°
---
#### l. ∠FEL = ?
Given: One angle is
68°
> ∠FEL = 90° − 68° =
22°
✔ Answer: 22°
---
✔ Final Answers Summary:
| Letter | Angle | Measure |
|--------|-------------|---------|
| a | ∠ABC | 53° |
| b | ∠PNO | 62° |
| c | ∠LJK | 38° |
| d | ∠NMP | 44° |
| e | ∠PRS | 20° |
| f | ∠VWU | 36° |
| g | ∠KLT | 75° |
| h | ∠RQS | 30° |
| i | ∠DCE | 67° |
| j | ∠CDA | 72° |
| k | ∠EFG | 59° |
| l | ∠FEL | 22° |
---
📌 Explanation Recap:
- All these problems involve finding the
missing angle in a pair of complementary angles.
- Since complementary angles sum to
90°, subtract the given angle from 90° to get the missing one.
- The diagrams show a right angle split into two parts — one labeled, one not — so the unlabeled one is the complement.
Let me know if you'd like a printable version or visual explanation!
Parent Tip: Review the logic above to help your child master the concept of complementary and supplementary worksheet.
