Applying Vertical Angle Relationships in Diagrams

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 11 | Questions: 20 | Updated: Jan 16, 2026
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1) In the diagram, ∠1 = 80°. What is the measure of the vertical angle to ∠1?

Explanation

Vertical angles are congruent.

So, the vertical angle to ∠1 = 80°.

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About This Quiz
Applying Vertical Angle Relationships In Diagrams - Quiz

Ready to crack some angle puzzles? Take this quiz and see how fast you can find vertical angles hiding in geometry diagrams. Along the way, you’ll practice using their special “always equal” rule and mix in challenges with linear pairs and supplementary angles. Each question helps you get better at... see morefinding missing measures while keeping your problem-solving sharp.
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2) At an intersection, ∠A and ∠B are vertical. ∠B is complementary to ∠C. If m∠A = 4x + 6 and m∠C = x + 24, what is m∠A?

Explanation

Step 1: ∠A = ∠B (vertical).

Step 2: ∠B + ∠C = 90° (complementary).

Step 3: (4x + 6) + (x + 24) = 90 → 5x + 30 = 90 → x = 12.

Step 4: ∠A = 4(12) + 6 = 54°.°.

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3) Two streets intersect, forming four angles. One angle measures 62°. What is the measure of the vertical angle across from it?

Explanation

Vertical angles are equal.

So, the opposite angle = 62°.

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4) If ∠1 = 75°, and ∠3 is its vertical angle, what is ∠3?

Explanation

Vertical angles are always equal → ∠3 = 75°.

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5) Two lines intersect. One angle is 125°. What is its vertical angle?

Explanation

Vertical angles are equal. So, both measure 125°.

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6) Two lines intersect. One angle is 118°. What are the measures of the other three angles?

Explanation

Step 1: Vertical opposite = 118°.

Step 2: Adjacent = 180 − 118 = 62°.

Step 3: Opposite to 62° = 62°.

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7) At an intersection, ∠x = 90°. What is the vertical angle to ∠x?

Explanation

When lines intersect forming right angles, all four angles = 90°.

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8) If ∠y = 137°, what is the measure of its vertical angle?

Explanation

Vertical angles are equal → vertical = 137°.

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9) In the diagram, ∠1 = (2x + 10)° and ∠3 = (3x – 20)°. If ∠1 and ∠3 are vertical, what is x?

Explanation

Step 1: Set equal → 2x + 10 = 3x – 20.

Step 2: Simplify → x = 30.

Step 3: Substitute → 2(30) + 10 = 70°.

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10) Two vertical angles are marked ∠A = 120° and ∠B. What is ∠B?

Explanation

Vertical angles are equal.

So, ∠B = 120°.

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11) Two lines intersect at point OOO. Angles are labeled ∠1, ∠2, ∠3, ∠4 in order around O. Which option correctly lists all vertical pairs and all linear pairs?

Explanation

Vertical pairs are opposite: (1,3) and (2,4). Linear pairs are adjacent: (1,2), (2,3), (3,4), (4,1).

So, the vertical pairs are (1,3) and (2,4), and the linear pairs are (1,2), (2,3), (3,4), (4,1).

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12) Two lines intersect. ∠1 = (4x – 15)°, ∠2 = (2x + 25)°. If they are vertical angles, what is ∠1?

Explanation

Vertical: 4x − 15 = 2x + 25 → 2x = 40 → x = 20.

Then ∠1 = 4(20) − 15 = 65.

The measure of ∠1 is 65°.

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13) If one angle is 15°, what is its vertical angle?

Explanation

Vertical angles are equal, so both are 15°.

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14) Which of the following statements about vertical angles is true?

Explanation

Vertical angles sit opposite each other and are congruent.

So, they are opposite and congruent.

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15) In the diagram, ∠A = 100°. Which angle is congruent to ∠A?

Explanation

Vertical angles are congruent → the one across from ∠A equals 100°.

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16) In the diagram, ∠1 = 70°. Which angle is vertical to ∠1?

Explanation

Vertical angles are opposite each other when two lines cross.

So, if ∠1 = 70°, the angle directly across (∠4) is also 70°.

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17) ∠A and ∠C are vertical angles. If ∠A = 95°, what is ∠C?

Explanation

Vertical angles are always congruent.

Step 1: Set them equal → ∠A = ∠C.

Step 2: Substitute → ∠C = 95°.

Final Answer: ∠C = 95°

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18) Two intersecting lines form four angles labeled ∠1, ∠2, ∠3, and ∠4. If ∠2 = 110°, what is ∠4?

Explanation

Vertical angles are equal in measure.

Step 1: ∠2 and ∠4 are opposite each other.

Step 2: So ∠4 = 110°.

Final Answer: ∠4 = 110°

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19) Two lines intersect. One angle measures 2x+14 and its vertical angle measures 5x−31. What is the measure of an angle adjacent to them?

Explanation

Vertical angles are equal. So,

Step 1: 2x + 14 = 5x − 31

Step 2: 45 = 3x → x = 15.

Step 3: Substitute → 2(15) + 14 = 44°.

Adjacent angles form a linear pair → 180 − 44 = 136°.

Submit
20) At an intersection, ∠M = 45°. Which angle is its vertical angle?

Explanation

Vertical angles are the pair across from each other, not beside.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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In the diagram, ∠1 = 80°. What is the measure of the vertical...
At an intersection, ∠A and ∠B are vertical. ∠B is...
Two streets intersect, forming four angles. One angle measures...
If ∠1 = 75°, and ∠3 is its vertical angle, what is ∠3?
Two lines intersect. One angle is 125°. What is its vertical...
Two lines intersect. One angle is 118°. What are the measures of...
At an intersection, ∠x = 90°. What is the vertical angle to...
If ∠y = 137°, what is the measure of its vertical angle?
In the diagram, ∠1 = (2x + 10)° and ∠3 = (3x –...
Two vertical angles are marked ∠A = 120° and ∠B. What is...
Two lines intersect at point OOO. Angles are labeled ∠1, ∠2,...
Two lines intersect. ∠1 = (4x – 15)°, ∠2 = (2x +...
If one angle is 15°, what is its vertical angle?
Which of the following statements about vertical angles is true?
In the diagram, ∠A = 100°. Which angle is congruent to ∠A?
In the diagram, ∠1 = 70°. Which angle is vertical to ∠1?
∠A and ∠C are vertical angles. If ∠A = 95°, what is...
Two intersecting lines form four angles labeled ∠1, ∠2,...
Two lines intersect. One angle measures 2x+14 and its vertical angle...
At an intersection, ∠M = 45°. Which angle is its vertical...
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