The image you've uploaded is a
completed worksheet titled *"Angles of Triangles: Interior Angles of Triangles Math Worksheet 1"*, and it includes an
answer key. The task is to
find the missing angle in each triangle, using the fact that:
>
✔ The sum of the interior angles in any triangle is always 180°.
Let’s go through each problem step by step, verify the solutions, and explain the reasoning.
---
🔷 Problem 1:
- Given angles: 49° and 90°
- Find angle C
Solution:
$$
C = 180^\circ - 49^\circ - 90^\circ = 41^\circ
$$
✔ Correct.
---
🔷 Problem 2:
- Given angles: 63° and 63°
- Find angle F
Solution:
$$
F = 180^\circ - 63^\circ - 63^\circ = 54^\circ
$$
✔ Correct.
---
🔷 Problem 3:
- Given angles: 41° and 80°
- Find angle A
Solution:
$$
A = 180^\circ - 41^\circ - 80^\circ = 59^\circ
$$
✔ Correct.
---
🔷 Problem 4:
- Given angles: 47° and 58°
- Find angle B
Solution:
$$
B = 180^\circ - 47^\circ - 58^\circ = 75^\circ
$$
✔ Correct.
---
🔷 Problem 5:
- Given angles: 114° and 33°
- Find angle D
Solution:
$$
D = 180^\circ - 114^\circ - 33^\circ = 33^\circ
$$
✔ Correct.
Note: This triangle has two equal angles (33°), so it's
isosceles.
---
🔷 Problem 6:
- Given angles: 47° and 36°
- Find angle J
Solution:
$$
J = 180^\circ - 47^\circ - 36^\circ = 97^\circ
$$
✔ Correct.
This is an
obtuse triangle since one angle is greater than 90°.
---
🔷 Problem 7:
- Given angles: 53° and 90°
- Find angle G
Solution:
$$
G = 180^\circ - 90^\circ - 53^\circ = 37^\circ
$$
✔ Correct.
This is a
right triangle with a right angle at the vertex labeled 90°.
---
🔷 Problem 8:
- Given angles: 52° and 43°
- Find angle E
Solution:
$$
E = 180^\circ - 52^\circ - 43^\circ = 85^\circ
$$
✔ Correct.
---
##
✔ Summary of All Answers:
| Triangle | Missing Angle | Calculation |
|--------|---------------|------------|
| 1 | C = 41° | 180 - 49 - 90 |
| 2 | F = 54° | 180 - 63 - 63 |
| 3 | A = 59° | 180 - 41 - 80 |
| 4 | B = 75° | 180 - 47 - 58 |
| 5 | D = 33° | 180 - 114 - 33 |
| 6 | J = 97° | 180 - 47 - 36 |
| 7 | G = 37° | 180 - 90 - 53 |
| 8 | E = 85° | 180 - 52 - 43 |
---
## 📌 Key Concept:
All problems use the
Triangle Angle Sum Theorem:
> The sum of the interior angles of a triangle is always
180 degrees.
So, if two angles are known:
$$
\text{Missing angle} = 180^\circ - \text{Angle 1} - \text{Angle 2}
$$
---
##
✔ Final Note:
The worksheet is correctly solved. All answers match the calculations, and the
answer key provided is accurate.
Let me know if you'd like a version without answers or want practice problems!
Parent Tip: Review the logic above to help your child master the concept of triangle properties worksheet.
