Applying Vertical Angle Relationships in Diagrams

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7049 | Total Attempts: 9,519,298
| Questions: 20
Please wait...
Question 1 / 20
0 %
0/100
Score 0/100
1) In the diagram, ∠1 = 80°. What is the measure of the vertical angle to ∠1?

Explanation

Vertical angles are equal.

So, the vertical angle also measures 80°.

The vertical angle to ∠1 is 80°.

Submit
Please wait...
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. see less

2)
We’ll put your name on your report, certificate, and leaderboard.
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

A and B are vertical, so A = B. B is complementary to C: B + C = 90.

Set 4x + 6 = 90 − (x + 24) → 4x + 6 = 66 − x → 5x = 60 → x = 12 → m∠A = 4(12) + 6 = 54.

The measure of ∠A is 54°.

Submit
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 is 62°.

The vertical angle measures 62.

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

Explanation

Vertical angles are equal.

So, ∠3 = 75°.

The measure of ∠3 is 75°.

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

Explanation

Vertical angles are equal.

So, the vertical angle is 125°.

The vertical angle measures 125°.

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

Explanation

Vertical angles match: the opposite is 118°. Adjacent angles are supplementary: 180 − 118 = 62°.

So, the other three are 62°, 118°, and 62°.

The other three angles are 62°, 118°, and 62°.

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

Explanation

Vertical angles are equal.

So, vertical to 90° is 90°.

The vertical angle measures 90°.

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

Explanation

Vertical angles are equal.

So, the vertical angle is 137°.

The vertical angle measures 137°.

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

Explanation

Vertical: 2x + 10 = 3x − 20 → x = 30.

So, x = 30.

The value of x is 30.

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

Explanation

Vertical angles are equal.

So, ∠B = 120°.

The measure of ∠B is 120°.

Submit
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, that’s the correct listing.

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

Submit
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°.

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

Explanation

Vertical angles are equal.

So, the vertical angle is 15°.

The vertical angle measures 15°.

Submit
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.

The true statement is they are opposite and congruent.

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

Explanation

Only the vertical angle is congruent to ∠A.

So, choose the vertical angle.

The angle congruent to ∠A is the vertical angle.

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

Explanation

Vertical angles are opposite each other at the intersection.

So, the angle opposite ∠1 is ∠3.

The vertical angle to ∠1 is ∠3.

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

Explanation

Vertical angles are equal.

So, ∠C = 95°.

The measure of ∠C is 95°.

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

Explanation

Vertical angles are equal and lie opposite each other.

So, ∠4 = ∠2 = 110°.

The measure of ∠4 is 110°.

Submit
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: 2x + 14 = 5x − 31 → 45 = 3x → x = 15.

Each vertical angle = 2(15) + 14 = 44°. Adjacent angles form a linear pair: 180 − 44 = 136.

An adjacent angle measures 136°.

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

Explanation

A vertical angle is directly across from the given angle.

So, it is the one across from ∠M.

The vertical angle to ∠M is the angle across from ∠M.

Submit
View My Results

Quiz Review Timeline (Updated): Oct 12, 2025 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Oct 12, 2025
    Quiz Edited by
    ProProfs Editorial Team
  • Sep 12, 2025
    Quiz Created by
    Thames
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
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...
Alert!

Back to Top Back to top
Advertisement