5th Grade Geometry - Free Printable

Let's solve each of the problems on the worksheet titled "ANGLES TO 90° SHEET 1". The goal is to mark the missing angles in each diagram, remembering that:

> A right angle = 90°

We are told that some angles are drawn to scale, so we can use visual estimation where helpful, but we should also apply angle rules.

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1)

We have a right angle (90°), and one angle is marked as 35°. The two angles together make up the right angle.

So:
$$
\text{Missing angle} = 90^\circ - 35^\circ = 55^\circ
$$

✔ Answer: 55°

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2)

This shows a right angle split into two parts: one is 68°, and the other is unknown.

$$
\text{Missing angle} = 90^\circ - 68^\circ = 22^\circ
$$

✔ Answer: 22°

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3)

Here, there’s a right angle (90°), and one angle is 47°. The missing angle is the rest of the right angle.

$$
\text{Missing angle} = 90^\circ - 47^\circ = 43^\circ
$$

✔ Answer: 43°

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4)

The diagram shows a right angle (90°), and one angle is 60°.

$$
\text{Missing angle} = 90^\circ - 60^\circ = 30^\circ
$$

✔ Answer: 30°

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5)

This is a straight line with a right angle at the corner. There is an angle labeled 50°, and another angle adjacent to it forming a right angle.

Wait — actually, looking carefully: it appears that the angle between the two lines is 50°, and we're to find the missing angle that completes the right angle.

But wait — the diagram shows a right angle formed by two lines, and a 50° angle inside it? That doesn’t add up unless...

Actually, re-examining: this looks like a right angle split into two parts: one is 50°, and the other is unknown.

So:
$$
\text{Missing angle} = 90^\circ - 50^\circ = 40^\circ
$$

✔ Answer: 40°

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6)

This is more complex: a triangle with a right angle and one angle given as 53°. We need to find the third angle.

In any triangle, the sum of angles is 180°.

We already have:
- One angle = 90° (right angle)
- Another = 53°

So:
$$
\text{Third angle} = 180^\circ - 90^\circ - 53^\circ = 37^\circ
$$

✔ Answer: 37°

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✔ Final Answers:

| Question | Missing Angle |
|--------|----------------|
| 1) | 55° |
| 2) | 22° |
| 3) | 43° |
| 4) | 30° |
| 5) | 40° |
| 6) | 37° |

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🔍 Explanation Summary:

- In questions 1–5, we used the fact that two angles making a right angle must add to 90°.
- In question 6, we used the triangle angle sum rule: angles in a triangle add to 180°, and since one is a right angle (90°), the other two must add to 90°.

All answers are based on basic geometry principles.

Let me know if you'd like a visual explanation or help drawing the angles!