Let's solve the problem step by step.
---
🔷 Understanding Complementary Angles
Two angles are
complementary if their sum is
90°.
So, if one angle is given, its
complementary angle is:
$$
\text{Complementary angle} = 90^\circ - \text{Given angle}
$$
We need to find the complementary angle for each of the given angles in the diagrams.
---
Now, let's go through each diagram and identify the
angle at point $ x $ (which is the vertex), and then compute its
complement.
---
✔ Diagram 1:
- Angle shown: $ 36^\circ $
- Complementary angle:
$$
90^\circ - 36^\circ = 54^\circ
$$
>
✔ Answer: 54°
---
✔ Diagram 2:
- Angle shown: $ 40^\circ $
- Complementary angle:
$$
90^\circ - 40^\circ = 50^\circ
$$
>
✔ Answer: 50°
---
✔ Diagram 3:
- Angle shown: $ 25^\circ $
- Complementary angle:
$$
90^\circ - 25^\circ = 65^\circ
$$
>
✔ Answer: 65°
---
✔ Diagram 4:
- Angle shown: $ 70^\circ $
- Complementary angle:
$$
90^\circ - 70^\circ = 20^\circ
$$
>
✔ Answer: 20°
---
✔ Diagram 5:
- Angle shown: $ 75^\circ $
- Complementary angle:
$$
90^\circ - 75^\circ = 15^\circ
$$
>
✔ Answer: 15°
---
✔ Diagram 6:
- Angle shown: $ 85^\circ $
- Complementary angle:
$$
90^\circ - 85^\circ = 5^\circ
$$
>
✔ Answer: 5°
---
✔ Diagram 7:
- Angle shown: $ 20^\circ $
- Complementary angle:
$$
90^\circ - 20^\circ = 70^\circ
$$
>
✔ Answer: 70°
---
✔ Diagram 8:
- Angle shown: $ 50^\circ $
- Complementary angle:
$$
90^\circ - 50^\circ = 40^\circ
$$
>
✔ Answer: 40°
---
✔ Final Answers:
| Diagram | Given Angle | Complementary Angle |
|--------|-------------|---------------------|
| 1 | 36° |
54° |
| 2 | 40° |
50° |
| 3 | 25° |
65° |
| 4 | 70° |
20° |
| 5 | 75° |
15° |
| 6 | 85° |
5° |
| 7 | 20° |
70° |
| 8 | 50° |
40° |
---
📌 Summary:
The task asks us to
identify the angle of the complementary angle for each given angle. Since all the given angles are less than 90°, they all have complements.
Each answer is simply:
$$
\boxed{90^\circ - \text{given angle}}
$$
---
✔ So, the
complementary angles are:
- 54°, 50°, 65°, 20°, 15°, 5°, 70°, 40° respectively.
Let me know if you'd like these written out in a specific format or boxed!
Parent Tip: Review the logic above to help your child master the concept of 7th grade angles worksheet.
