Let's solve each of the problems on
"Angles to 90° Sheet 1" step by step.
We are given that:
- A right angle is equal to
90°.
- We need to
mark and draw missing angles so that the total angle at each point adds up to
90°.
- The angles are drawn to scale, so we can use visual estimation as a guide.
---
1)
We have two adjacent angles forming a right angle (90°). One angle is labeled
35°.
We need to find the missing angle.
Calculation:
$$
\text{Missing angle} = 90^\circ - 35^\circ = 55^\circ
$$
✔ So, the missing angle is
55°.
---
2)
This shows two angles: one is
40°, and another is
25°, with a third angle in between.
Wait — actually, looking at the diagram:
It appears that there are
three angles meeting at a point, but they form a
right angle (90°). The two known angles are
40° and
25°.
So:
$$
\text{Total of known angles} = 40^\circ + 25^\circ = 65^\circ
$$
$$
\text{Missing angle} = 90^\circ - 65^\circ = 25^\circ
$$
✔ So, the missing angle is
25°.
Wait — double-check: Is this correct?
But look again: The diagram seems to show
two lines forming a right angle, and two rays splitting it into three parts: 40°, ?, and 25°? But if the total is 90°, then:
$$
40^\circ + x + 25^\circ = 90^\circ \Rightarrow x = 25^\circ
$$
Yes — so the middle angle is
25°.
✔ Missing angle =
25°
---
3)
This shows a right angle split into two parts: one is
60°, and the other is missing.
$$
\text{Missing angle} = 90^\circ - 60^\circ = 30^\circ
$$
✔ So, the missing angle is
30°.
---
4)
Here, a right angle is split into two angles: one is
70°, and the other is missing.
$$
\text{Missing angle} = 90^\circ - 70^\circ = 20^\circ
$$
✔ So, the missing angle is
20°.
---
5)
This one looks more complex: a right angle (90°) is split into
three angles: 30°, ?, and 20°.
So:
$$
30^\circ + x + 20^\circ = 90^\circ \Rightarrow x = 40^\circ
$$
✔ Missing angle =
40°
---
6)
Now, this one has
two angles: one is
15°, and the other is
?, and they make up a
right angle.
$$
\text{Missing angle} = 90^\circ - 15^\circ = 75^\circ
$$
✔ So, the missing angle is
75°.
---
✔ Final Answers:
| Question | Missing Angle |
|--------|----------------|
| 1) |
55° |
| 2) |
25° |
| 3) |
30° |
| 4) |
20° |
| 5) |
40° |
| 6) |
75° |
---
🔍 Summary:
In all cases, we used the fact that:
> The sum of angles forming a right angle is
90°.
We subtracted the known angle(s) from 90° to find the missing one.
For multiple angles, we added the known ones and subtracted from 90°.
---
📝 Instructions for Drawing:
- Use a protractor to measure and draw the missing angle.
- Ensure the new ray divides the right angle correctly.
- Label the angle with the calculated degree.
---
✔ All angles solved!
Let me know if you'd like a printable version or help drawing them!
Parent Tip: Review the logic above to help your child master the concept of 5th grade angle worksheet.
