Solving Equations with Vertical Angles

Grade 8th

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Quizzes Created: 11119 | Total Attempts: 9,762,531

| Attempts: 13 | Questions: 20 | Updated: Jan 16, 2026

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1) If ∠x = 3y + 5 and ∠y = 50, and the two angles are vertical, what is the value of y?

Step 1: Vertical angles are equal, so set 3y + 5 = 50.

Step 2: Subtract 5 → 3y = 45.

Step 3: Divide by 3 → y = 15.

Final Answer: y = 15

Explanation

Step 1: Vertical angles are equal, so set 3y + 5 = 50.

Step 2: Subtract 5 → 3y = 45.

Step 3: Divide by 3 → y = 15.

Final Answer: y = 15

Submit

About This Quiz

Solving Equations With Vertical Angles - Quiz

Can you combine algebra and geometry? In this quiz, you’ll solve equations based on the fact that vertical angles are always equal. You’ll begin with straightforward setups and then tackle multi-step problems involving angles that form straight lines. Using what you know about vertical and supplementary angles, you’ll find missing... see morevalues while seeing how algebra and geometry work hand in hand.
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2)

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2) ∠1 and ∠2 are vertical angles. ∠1 = (11n – 15)°, ∠2 = (7n + 21)°. Solve for n.

Vertical angles are equal. So,

Step 1: Set equal → 11n – 15 = 7n + 21.

Step 2: Simplify → 4n = 36.

Step 3: Divide → n = 9, and substitute → 11(9) – 15 = 84°.

Final Answer: n = 9, and each angle = 84°.

Explanation

Submit

3) Two vertical angles are expressed as (2x + 25)° and (75 + x)°. Find x.

Vertical angles are equal. So,

Step 1: Set equal → 2x + 25 = 75 + x.

Step 2: Simplify → x = 50.

Step 3: Substitute → (2×50 + 25) = 125°, (75 + 50) = 125°.

Final Answer: x = 50, and each angle = 125°.

Explanation

Submit

4) Two vertical angles are given as (2x + 10)° and (4x – 30)°. Find the measure of each angle.

40°

50°

55°

60°

Step 1: Vertical angles are equal → 2x + 10 = 4x – 30.

Step 2: Simplify → 40 = 2x → x = 20.

Step 3: Substitute → 2(20) + 10 = 50.

Explanation

Step 1: Vertical angles are equal → 2x + 10 = 4x – 30.

Step 2: Simplify → 40 = 2x → x = 20.

Step 3: Substitute → 2(20) + 10 = 50.

Submit

5) If vertical angles ∠R = (4x + 12)° and ∠S = (6x – 18)°, find the value of x.

Vertical angles are equal. So,

Step 1: Set equal → 4x + 12 = 6x – 18.

Step 2: Simplify → 2x = 30.

Step 3: Divide → x = 15, and substitute → 4(15) + 12 = 72°.

Final Answer: x = 15, and each angle = 72°.

Explanation

Submit

6) If ∠A = (x + 12)° and ∠B = (2x – 18)°, and ∠A = ∠B, find the measure of each.

38°

42°

56°

60°

Vertical angles are equal. So,

Step 1: Set equal → x + 12 = 2x – 18.

Step 2: Simplify → x = 30.

Step 3: Substitute → (30 + 12) = 42°, (2×30 – 18) = 42°.

Final Answer: x = 30, and each angle = 42°.

Explanation

Submit

7) If ∠x = (5m + 7)° and ∠y = (6m – 3)°, find the angle measure if x and y are vertical.

47°

52°

57°

62°

Vertical angles are equal. So,

Step 1: Set equal → 5m + 7 = 6m – 3.

Step 2: Simplify → m = 10.

Step 3: Substitute → 5(10) + 7 = 57°.

Final Answer: Each angle = 57°

Explanation

Vertical angles are equal. So,

Step 1: Set equal → 5m + 7 = 6m – 3.

Step 2: Simplify → m = 10.

Step 3: Substitute → 5(10) + 7 = 57°.

Final Answer: Each angle = 57°

Submit

8) ∠P = (6k – 12)°, ∠Q = (4k + 8)°. If P and Q are vertical, find k.

Vertical angles are equal. So,

Step 1: Set equal → 6k – 12 = 4k + 8.

Step 2: Simplify → 2k = 20.

Step 3: Divide → k = 10.

Final Answer: k = 10

Explanation

Vertical angles are equal. So,

Step 1: Set equal → 6k – 12 = 4k + 8.

Step 2: Simplify → 2k = 20.

Step 3: Divide → k = 10.

Final Answer: k = 10

Submit

9) Vertical angles are written as (12 + 2x)° and (3x – 6)°. What is the measure of the angles?

18°

30°

48°

55°

Vertical angles are equal. So,

Step 1: Set equal → 12 + 2x = 3x – 6.

Step 2: Simplify → x = 18.

Step 3: Substitute → 12 + 2(18) = 48°.

Final Answer: Each angle = 48°

Explanation

Vertical angles are equal. So,

Step 1: Set equal → 12 + 2x = 3x – 6.

Step 2: Simplify → x = 18.

Step 3: Substitute → 12 + 2(18) = 48°.

Final Answer: Each angle = 48°

Submit

10) Two vertical angles are (4b – 5)° and (3b + 10)°. Find the measure of each angle.

35°

40°

45°

55°

Vertical angles are equal. So,

Step 1: Set equal → 4b – 5 = 3b + 10.

Step 2: Simplify → b = 15.

Step 3: Substitute → (4×15 – 5) = 55° and (3×15 + 10) = 55°.

Final Answer: 15, and each angle = 55°.

Explanation

Submit

11) ∠M = (3a + 5)°, ∠N = (2a + 25)°. If ∠M and ∠N are vertical, then what is a?

Vertical angles are equal. So,

Step 1: Set equal → 3a + 5 = 2a + 25.

Step 2: Simplify → a = 20.

Step 3: Substitute → ∠M = 3(20) + 5 = 65° and ∠N = 2(20) + 25 = 65°.

Explanation

Vertical angles are equal. So,

Step 1: Set equal → 3a + 5 = 2a + 25.

Step 2: Simplify → a = 20.

Step 3: Substitute → ∠M = 3(20) + 5 = 65° and ∠N = 2(20) + 25 = 65°.

Submit

12) If one vertical angle is (7x – 25)° and the other is (5x + 15)°, find the value of x.

Vertical angles are equal. So,

Step 1: Set equal → 7x – 25 = 5x + 15.

Step 2: Simplify → 2x = 40.

Step 3: Divide → x = 20.

Explanation

Vertical angles are equal. So,

Step 1: Set equal → 7x – 25 = 5x + 15.

Step 2: Simplify → 2x = 40.

Step 3: Divide → x = 20.

Submit

13) Two vertical angles are represented as (x + 30)° and (2x – 60)°. What is the value of x?

Vertical angles are equal. So,

Step 1: Set equal → x + 30 = 2x – 60.

Step 2: Simplify → 90 = x.

Step 3: Substitute to check → (90 + 30) = 120°, both match.

Explanation

Vertical angles are equal. So,

Step 1: Set equal → x + 30 = 2x – 60.

Step 2: Simplify → 90 = x.

Step 3: Substitute to check → (90 + 30) = 120°, both match.

Submit

14) ∠1 = (6y – 20)°, ∠2 = (4y + 10)°. If ∠1 and ∠2 are vertical, then what is y?

Vertical angles are equal. So,

Step 1: Set equal → 6y – 20 = 4y + 10.

Step 2: Simplify → 2y = 30.

Step 3: Divide → y = 15.

Explanation

Vertical angles are equal. So,

Step 1: Set equal → 6y – 20 = 4y + 10.

Step 2: Simplify → 2y = 30.

Step 3: Divide → y = 15.

Submit

15) ∠1 and ∠2 are vertical. ∠2 and ∠3 form a linear pair. If ∠1 = 3x + 6 and ∠3 = x + 66, find the measures of ∠1, ∠2, ∠3 (in that order).

87°, 87°, 93°

93°, 93°, 87

87°, 93°, 93°

90°, 90°, 90°

Vertical angles are equal. So,

Step 1: ∠1 = ∠2 = 3x + 6, and ∠2 + ∠3 = 180.

Step 2: Substitute → (3x + 6) + (x + 66) = 180 → 4x + 72 = 180 → x = 27.

Step 3: ∠1 = 3(27) + 6 = 87°, ∠3 = 93°.

Final Answer: ∠1 = 87°, ∠2 = 87°, ∠3 = 93°

Explanation

Submit

16) ∠1 and ∠2 are vertical. ∠2 and ∠3 form a linear pair. If ∠1 = 4y + 8 and ∠3 = 2y + 52, find the measures of ∠1, ∠2, ∠3 (in that order).

92°, 92°, 88°

88°, 92°, 88°

90°, 90°, 90°

88°, 88°, 92°

Vertical angles are equal. So,

Step 1: ∠1 = ∠2 = 4y + 8 and ∠2 + ∠3 = 180.

Step 2: Substitute → (4y + 8) + (2y + 52) = 180 → 6y + 60 = 180 → y = 20.

Step 3: Substitute → ∠1 = 4(20) + 8 = 88°, ∠3 = 2(20) + 52 = 92°.

Final Answer: ∠1 = 88°, ∠2 = 88°, ∠3 = 92°.

Explanation

Submit

17) If vertical angles are expressed as (x – 10)° and (2x – 40)°, what is x?

Vertical angles are equal. So,

Step 1: Set equal → x + 30 = 2x – 60.

Step 2: Simplify → x = 90.

Step 3: Substitute → (90 + 30) = 120°, (2×90 – 60) = 120°.

Final Answer: x = 90, and each angle = 120°.

Explanation

Submit

18) Two vertical angles are (x – 3)° and (2x – 23)°. Find the measure of each.

10°

15°

17°

20°

Vertical angles are equal. So,

Step 1: Set equal → x – 3 = 2x – 23.

Step 2: Simplify → x = 20.

Step 3: Substitute → (20 – 3) = 17°, (2×20 – 23) = 17°.

Final Answer: x = 20, and each angle = 17°.

Explanation