5th Grade Geometry - Free Printable

It looks like you've uploaded a worksheet titled "ANGLES ON A STRAIGHT LINE", which contains several problems involving angles that lie on a straight line. The key concept here is:

> The sum of angles on a straight line is 180°.

Let’s go through each problem one by one and solve them step-by-step.

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Problem 1:

We have two angles:
- One angle is labeled 75°
- The other is labeled x

Since they are on a straight line:

$$
75^\circ + x = 180^\circ
$$

$$
x = 180^\circ - 75^\circ = 105^\circ
$$

✔ Answer: 105°

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Problem 2:

One angle is 96°, the other is x

$$
96^\circ + x = 180^\circ
$$

$$
x = 180^\circ - 96^\circ = 84^\circ
$$

✔ Answer: 84°

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Problem 3:

One angle is 72°, the other is x

$$
72^\circ + x = 180^\circ
$$

$$
x = 180^\circ - 72^\circ = 108^\circ
$$

✔ Answer: 108°

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Problem 4:

One angle is 112°, the other is x

$$
112^\circ + x = 180^\circ
$$

$$
x = 180^\circ - 112^\circ = 68^\circ
$$

✔ Answer: 68°

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Problem 5:

One angle is 120°, the other is x

$$
120^\circ + x = 180^\circ
$$

$$
x = 180^\circ - 120^\circ = 60^\circ
$$

✔ Answer: 60°

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Problem 6:

One angle is 134°, the other is x

$$
134^\circ + x = 180^\circ
$$

$$
x = 180^\circ - 134^\circ = 46^\circ
$$

✔ Answer: 46°

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✔ Summary of Answers:

1. 105°
2. 84°
3. 108°
4. 68°
5. 60°
6. 46°

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🔍 Explanation:

All these problems use the fundamental rule:
> Angles on a straight line add up to 180°.

So, whenever you see two angles forming a straight line (i.e., they are adjacent and together make a straight angle), just subtract the known angle from 180° to find the unknown one.

This principle is crucial in geometry and helps solve many real-world problems involving lines, roads, or structures where angles must align.

Let me know if you'd like this turned into a printable answer sheet!