Geometry and proof · Ages 12–13

Angles with an unknown worksheet

Part of: Angles & parallel lines

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Geometry and proof · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Two straight lines cross; the two angles written with x are vertically opposite. x =
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2.The two angles lie on a straight line. x + 5x = 180, x = 180, x = .
Fill in each blank
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3.The two angles lie on a straight line. x =
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4.The two angles lie on a straight line. x + 4x = 180, x = 180, x = .
Fill in each blank
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5.The two angles lie on a straight line. x + 8x = 180, x = 180, x = .
Fill in each blank
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6.Two straight lines cross, as shown. x =
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7.The three angles lie on a straight line. x =
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8.The three angles go round one point. How many degrees is the largest?
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9.Two straight lines cross; the two angles written with x are vertically opposite. How many degrees is each of them?
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13.Four angles go round one point: x°, 2x°, 4x° and 143°. What is x?
Working:
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14.Two straight lines cross. A pair of vertically opposite angles are (5x − 26)° and (3x + 34)°. What is x?
Working:
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15.To find x, the first line is 2x + 9 = 4x − 21 (______). Which reason goes in the blank?
- A. ∠s at a pt.
- B. vert. opp. ∠s
- C. adj. ∠s on st. line
- D. alt. ∠s, AB // CD
Choose the right answer
Working:
Answer:
16.The two angles lie on a straight line. Find x: put the steps in order.
- A. x = 25
- B. 4x + 9 + 2x + 21 = 180 (adj. ∠s on st. line)
- C. 6x = 150
- D. 6x + 30 = 180
Write the letters in the right order
Working:
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17.Two straight lines cross, as shown; the two angles written with x are vertically opposite. What is y?
Working:
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18.The two angles marked are vertically opposite. 2x + 33 = 5x − 57, x = , and each angle = °.
Fill in each blank
Working:
Answer:

Show the answers and working

Angles with an unknown worksheet: Answers and working

1. 25
Vertically opposite angles are equal: 2x + 15 = 5x − 60 (vert. opp. ∠s), 3x = 15 + 60 = 75, x = 25.
2. 6, 30
x° and 5x° add to 180° (adj. ∠s on st. line): x + 5x = 6x = 180, x = 180 ÷ 6 = 30.
3. 20
(5x + 14) + 66 = 180 (adj. ∠s on st. line), 5x = 180 − 66 − 14 = 100, x = 20.
4. 5, 36
x° and 4x° add to 180° (adj. ∠s on st. line): x + 4x = 5x = 180, x = 180 ÷ 5 = 36.
5. 9, 20
x° and 8x° add to 180° (adj. ∠s on st. line): x + 8x = 9x = 180, x = 180 ÷ 9 = 20.
6. 14
First the relation: if (5x + 40)° faces 70°, they are equal (vert. opp. ∠s); if side by side, they add to 180° (adj. ∠s on st. line). Here 5x + 40 = 110, 5x = 70, x = 14.
7. 15
(3x + 26) + 4x + 49 = 180 (adj. ∠s on st. line), 7x = 180 − 26 − 49 = 105, x = 15.
8. 150°
(3x + 22) + (3x + 38) + (5x + 25) = 360 (∠s at a pt.), 11x = 275, x = 25. Put it back into each: 97°, 113°, 150°; the largest is 150°.
9. 62°
3x − 10 = 2x + 14 (vert. opp. ∠s), x = 24, x = 24. Put it back: 3 × 24 − 10 = 62, so each angle is 62°.

10. A. 2x + 6 = 5x − 66
The two angles face each other: vertically opposite, so equal. 2x + 6 = 5x − 66 (vert. opp. ∠s), which gives x = 24.
11. True
(2x + 5) + (3x + 45) = 180 (adj. ∠s on st. line), 5x = 130, x = 26.
12. False
(3x + 14) + (2x + 96) = 180 (adj. ∠s on st. line), 5x = 70, x = 14.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 31
The four add to 360 (∠s at a pt.): x + 2x + 4x + 143 = 360, 7x = 360 − 143, x = 31.
14. 30
Opposite angles are equal: 5x − 26 = 3x + 34, 2x = 34 + 26, x = 30. Check: both angles are 124°.
15. B. vert. opp. ∠s
The two angles face each other where the lines cross: vertically opposite, so the two are equal. It gives x = 15, each angle 39°.
16. B → D → C → A
The two lie on a straight line and add to 180: 4x + 9 + 2x + 21 = 180; collecting, 6x + 30 = 180, 6x = 150, x = 25.
17. 135°
Opposite angles are equal: 2x + 9 = 3x − 9, x = 18, so that angle is 45°. y lies on a line with it: y = 180° − 45° = 135° (adj. ∠s on st. line).
18. 30, 93
Vertically opposite angles are equal: 2x + 33 = 5x − 57; moving terms, 3x = 33 + 57, x = 30. Put it back: 2 × 30 + 33 = 93, so each angle is 93°.

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