Printable worksheet for students to practice calculating angles on a straight line, featuring multiple questions, diagrams, and a character named Mo explaining angle measurements.

Let's go through the "Calculating Angles on a Straight Line Worksheet" step by step and solve each question with clear explanations.

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1. How many degrees are in a straight angle (a straight line)?

✔ Answer: 180°
👉 A straight angle forms a straight line, and the total angle around a straight line is 180 degrees.

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2. How many degrees are in a right angle?

✔ Answer: 90°
👉 A right angle is exactly one-quarter of a full circle and measures 90 degrees.

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3. How many right angles would equal a straight angle?

✔ Answer: 2 right angles
👉 Since one right angle = 90°, then:
  90° + 90° = 180° → So, 2 right angles make a straight angle.

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4. Calculate the missing angles (x) below.

We use the rule: Angles on a straight line add up to 180°.

#### a)
Given: One angle = 45°
So:
  x = 180° − 45° = 135°

✔ Answer: 135°

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#### b)
Given: One angle = 110°
So:
  x = 180° − 110° = 70°

✔ Answer: 70°

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#### c)
Given: One angle = 90°
So:
  x = 180° − 90° = 90°

✔ Answer: 90°

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#### d)
Given: One angle = 160°
So:
  x = 180° − 160° = 20°

✔ Answer: 20°

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#### e)
There are two 45° angles shown. But they're both adjacent to angle x on a straight line.
Wait — let’s look carefully:

The diagram shows:
- A vertical line splitting the straight line into three parts?
But actually, it looks like two angles of 45° are on one side of x?

Wait — better interpretation: The straight line has:
- A red angle labeled x
- Then a yellow 45°
- Then another yellow 45°

But if all three are on a straight line, then:
  x + 45° + 45° = 180°
  x + 90° = 180°
  x = 90°

✔ Answer: 90°

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#### f)
Given: 30° and 120°, and we need to find x.

So:
  x + 30° + 120° = 180°
  x + 150° = 180°
  x = 30°

✔ Answer: 30°

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5. Mo is measuring two angles on a straight line. He says: "My angles measure 110° and 60°." Is he correct? Explain your answer.

Let’s check:
110° + 60° = 170° ≠ 180°

✘ No, Mo is not correct.
Because angles on a straight line must add up to 180°, but 110° + 60° = 170°, which is 10° short.

✔ Answer: No, because 110° + 60° = 170°, which is less than 180°. Angles on a straight line must total 180°.

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6. Angles x and y are two angles on a straight line.

So:
  x + y = 180°

#### a) Angle x is bigger than 100°. What could angle y measure?

If x > 100°, then since x + y = 180°,
  y = 180° − x
Since x > 100°, then y < 80°

So y must be less than 80°

✔ Example: If x = 110°, then y = 70°
Any value of y less than 80° is possible.

➡️ Answer: y could be any angle less than 80° (e.g., 70°, 60°, etc.)

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#### b) Angle x is bigger than 150° and is a multiple of 10. What could y measure?

Multiples of 10 greater than 150° and less than 180° (since x < 180°):

Possible values for x:
→ 160°, 170°

Now calculate y:

- If x = 160°, y = 180° − 160° = 20°
- If x = 170°, y = 180° − 170° = 10°

So y could be 10° or 20°

✔ Answer: y could be 10° or 20°

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#### c) Angle x and angle y are equal. What do they measure?

If x = y and x + y = 180°, then:

  x + x = 180°
  2x = 180°
  x = 90°

So both angles are 90°

✔ Answer: Both angles measure 90°

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| 1 | 180° |
| 2 | 90° |
| 3 | 2 right angles |
| 4a | 135° |
| 4b | 70° |
| 4c | 90° |
| 4d | 20° |
| 4e | 90° |
| 4f | 30° |
| 5 | No, because 110° + 60° = 170° ≠ 180° |
| 6a | y < 80° (e.g., 70°) |
| 6b | y = 10° or 20° |
| 6c | Both angles = 90° |

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