Let's solve each of the problems in the worksheet titled
"Find the Missing Angle 1". The goal is to find the missing angle in each triangle using the
Triangle Sum Theorem, which states:
>
The sum of the interior angles in any triangle is 180°.
We'll go through each problem step by step.
---
Problem 24
- Given angles: 35° and 90°
- Find the missing angle.
Solution:
$$
\text{Missing angle} = 180^\circ - 35^\circ - 90^\circ = 55^\circ
$$
✔ Answer: 55°
---
Problem 25
- Given angles: 40° and 60°
- Find the missing angle.
Solution:
$$
\text{Missing angle} = 180^\circ - 40^\circ - 60^\circ = 80^\circ
$$
✔ Answer: 80°
---
Problem 26
- Given angles: 50° and 90°
- Find the missing angle.
Solution:
$$
\text{Missing angle} = 180^\circ - 50^\circ - 90^\circ = 40^\circ
$$
✔ Answer: 40°
---
Problem 27
- Given angles: 75° and 30°
- Find the missing angle.
Solution:
$$
\text{Missing angle} = 180^\circ - 75^\circ - 30^\circ = 75^\circ
$$
✔ Answer: 75°
---
Summary of Answers:
| Problem | Missing Angle |
|--------|----------------|
| 24 | 55° |
| 25 | 80° |
| 26 | 40° |
| 27 | 75° |
---
Explanation:
In each case, we used the
Triangle Sum Theorem:
$$
\angle A + \angle B + \angle C = 180^\circ
$$
We subtracted the two known angles from 180° to find the third (missing) angle.
This method works for all triangles, whether they are right, acute, or obtuse — as long as you know two angles, you can always find the third.
✔ All angles are less than 180°, so no issues with external angles or reflex angles here.
Let me know if you'd like a visual explanation or want to check your answers!
Parent Tip: Review the logic above to help your child master the concept of find the missing angle worksheet.
