Identifying and Understanding Vertical Angles

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Cierra Henderson, MBA |
K-12 Expert
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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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Quizzes Created: 8157 | Total Attempts: 9,569,759
| Attempts: 13 | Questions: 20 | Updated: Jan 16, 2026
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1) If ∠A = 47°, what is the measure of its vertical angle?

Explanation

When lines cross, opposite angles are equal.

So, if one is 47°, its vertical angle is also 47°.

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About This Quiz
Identifying and Understanding Vertical Angles - Quiz

Are you ready to see how vertical angles can unlock geometry problems? In this quiz, you’ll explore how equal angles form whenever two lines intersect — and how that fact makes solving questions easier. You’ll practice spotting these angle pairs, work through equations with linear pairs, and apply them to... see morefind missing values. Step by step, you’ll gain confidence as you see how vertical angles simplify tricky geometry challenges!
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2) If ∠p = 72°, which of the following is also 72°?

Explanation

Vertical angles are opposite each other when lines intersect. They are always equal, so if ∠p = 72°, the vertical angle is also 72°.

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3) If ∠1 = 72°, which of the following is also 72°?

Explanation

Vertical angles are formed by intersecting lines and are always equal.

So, the angle opposite ∠1 is 72° as well.

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4) Which relationship is shown if two angles share a vertex and a side and their interiors do not overlap?

Explanation

When two angles share a vertex and a side but don’t overlap, they sit next to each other.

That makes them adjacent angles.

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5) If one angle formed by intersecting lines is 120°, what is the measure of its vertical angle?

Explanation

Opposite angles formed by intersecting lines are equal.

So, if one is 120°, its vertical pair is also 120°.

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6) At an intersection, one angle is 45°. What is the measure of the opposite angle?

Explanation

Vertical angles always have equal measures.

So, if one angle is 45°, the opposite one is also 45°.

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7) Two intersecting lines form four angles. If ∠x = 110°, what is the measure of the vertical angle to ∠x?

Explanation

Vertical angles are the pair across from each other when lines cross.

They are equal, so both are 110°.

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8) Vertical angles are formed when:

Explanation

When two lines cross, the opposite angles that face each other are vertical.

That’s the only way vertical angles form — by intersection.

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9) If ∠p = 88°, then the vertical angle to ∠p is:

Explanation

Vertical angles are equal because they share the same intersection lines.

So, both are 88°.

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10) If two lines intersect, how many pairs of vertical angles are formed?

Explanation

Two intersecting lines create four angles in total.

That gives two pairs of opposite (vertical) angles.

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11) Which property makes vertical angles useful in problem solving?

Explanation

Vertical angles are always equal in measure, which helps solve for unknown angles easily.

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12) Two lines intersect. One angle measures 3x + 12 and its vertical angle measures 2x + 52. What is the measure of an angle adjacent to them?

Explanation

Vertical angles are equal → 3x + 12 = 2x + 52 → x = 40.

So, each vertical angle = 3(40) + 12 = 132°.

Adjacent angles form a linear pair → 180 − 132 = 48° 

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13) When two lines intersect, the opposite (non-adjacent) angles are called: 

Explanation

When two lines cross, they form opposite angles that face each other.

Those opposite angles are called vertical angles, and they are always equal.

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14) If ∠A = 50°, what is the measure of the vertical angle to ∠A?

Explanation

When two lines cross, opposite angles are equal.

So, if ∠A = 50°, its vertical angle is also 50°.

Submit
15) Two lines intersect and form one angle of 95°. What is the measure of the vertical angle?

Explanation

Vertical angles are equal in measure.

If one angle is 95°, the angle directly across from it is also 95°.

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16) Which pair of angles are vertical?

Explanation

Vertical angles are the pair that are directly across from each other, not next to each other.

So, ∠3 and ∠4 are vertical.

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17) Two lines intersect to form ∠1,∠2,∠3,∠4 in order around the point. ∠1 and ∠2 are vertical. ∠2 and ∠3 form a linear pair. If m∠1 = 3y + 12 and m∠3 = y + 48, what is m∠1?

Explanation

Vertical angles are equal: ∠1 = ∠2.

Linear pair → ∠2 + ∠3 = 180°.

So, (3y + 12) + (y + 48) = 180 → 4y + 60 = 180 → y = 30.

m∠1 = 3(30) + 12 = 102°.

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18) Two lines cross. One of the angles is 160°. What is the measure of the vertical angle?

Explanation

Vertical angles face each other and always have the same measure.

So, if one is 160°, the opposite one is also 160°.

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19) If ∠x = 105°, then its vertical angle is:

Explanation

Vertical angles are always congruent.

So, both angles measure 105°.

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20) If one angle at an intersection is 30°, what is the measure of its vertical angle?

Explanation

Vertical angles are congruent.

If one is 30°, the opposite one must also be 30°.

Submit
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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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If ∠A = 47°, what is the measure of its vertical angle?
If ∠p = 72°, which of the following is also 72°?
If ∠1 = 72°, which of the following is also 72°?
Which relationship is shown if two angles share a vertex and a side...
If one angle formed by intersecting lines is 120°, what is the...
At an intersection, one angle is 45°. What is the measure of the...
Two intersecting lines form four angles. If ∠x = 110°, what is...
Vertical angles are formed when:
If ∠p = 88°, then the vertical angle to ∠p is:
If two lines intersect, how many pairs of vertical angles are formed?
Which property makes vertical angles useful in problem solving?
Two lines intersect. One angle measures 3x + 12 and its vertical angle...
When two lines intersect, the opposite (non-adjacent) angles are...
If ∠A = 50°, what is the measure of the vertical angle to...
Two lines intersect and form one angle of 95°. What is the measure...
Which pair of angles are vertical?
Two lines intersect to form ∠1,∠2,∠3,∠4 in order...
Two lines cross. One of the angles is 160°. What is the measure of...
If ∠x = 105°, then its vertical angle is:
If one angle at an intersection is 30°, what is the measure of its...
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