Vertical Angles Quiz: Master Vertical Angles Quiz

  • 7th Grade,
  • 8th Grade
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| Attempts: 19 | Questions: 20 | Updated: Dec 17, 2025
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1) If ∠A = 70°, what is the measure of its vertical angle?

Explanation

When two lines intersect, vertical angles are equal. So, if ∠A = 70°, its vertical angle is also 70°.

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About This Quiz
Vertical Angles Quiz: Master Vertical Angles Quiz - Quiz

How can vertical angles simplify your work with intersecting lines? In this quiz, you’ll explore how equal angle pairs appear whenever two lines cross and how that relationship unlocks many geometric problems. You’ll practice identifying vertical angle pairs, using algebra to solve for missing values, and connecting angle relationships to... see morediagrams. Step by step, you’ll see how vertical angles make complex intersections easier to interpret and how this one idea streamlines a variety of angle-based questions.
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2) Select all true statements about vertical angles.

Explanation

Vertical angles are opposite each other, congruent, and occur when two lines intersect. They do not share a common side and are not necessarily supplementary.

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3) The sum of all four angles formed by two intersecting lines is 360°.

Explanation

Two intersecting lines form four angles around a point, and the full rotation around a point is 360°.

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4) If one angle in an intersection is 110°, what is its vertical angle?

Explanation

Opposite (vertical) angles are equal. So, both measure 110°.

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5) All pairs of vertical angles are congruent.

Explanation

By definition, vertical angles are always equal in measure, no matter their size.

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6) Two lines intersect forming one 130° angle. What is the measure of its vertical angle?

Explanation

Vertical angles are equal, so the opposite angle is also 130°.

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7) Vertical angles can be both acute and obtuse at the same intersection.

Explanation

When two lines intersect, one pair of vertical angles can be acute (less than 90°) while the other pair is obtuse (more than 90°).

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8) Vertical angles are always supplementary.

Explanation

Vertical angles are congruent (equal in measure), not supplementary. Supplementary angles sum to 180°, but vertical angles are equal.

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9) Two lines intersect forming one angle of 120°. The vertical angle also measures ____.

Explanation

When lines intersect, opposite (vertical) angles are equal. So, the vertical angle is 120°.

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10) If ∠1 = 3x + 10 and ∠2 = 5x − 30, and the angles are vertical, find x.

Explanation

Since vertical angles are equal, 3x + 10 = 5x − 30 ⇒ 2x = 40 ⇒ x = 20. Substituting back, each angle = 3(20) + 10 = 70°, confirming equality.

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11) If one of two vertical angles measures 85°, what is the other angle?

Explanation

Vertical angles are always equal. So, both measure 85°.

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12) If ∠x = 2x + 20 and its vertical angle is 5x − 40, find x = __.

Explanation

Set equal since they are vertical: 2x + 20 = 5x − 40 ⇒ 3x = 60 ⇒ x = 20. Each angle = 2(20)+20 = 60°.

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

Explanation

Equating: 4y − 5 = 3y + 10 ⇒ y = 15. Substitute back: 4(15) − 5 = 55°. Each angle measures 55°.

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14) If one angle at an intersection is 45°, then the opposite vertical angle is __°.

Explanation

Vertical angles are congruent. If one angle is 45°, the opposite is also 45°.

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15) Two lines intersect. If ∠1 = 3x + 12 and ∠2 = 2x + 32 are vertical, what is x?

Explanation

Since ∠1 = ∠2, 3x + 12 = 2x + 32 ⇒ x = 20. Substitute back: ∠1 = 3(20)+12 = 72°, verifying equality.

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16) In a diagram, ∠A = 60°. What is the measure of its supplementary angle?

Explanation

Supplementary angles add to 180°. So, 180 − 60 = 120°.

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17) Select all correct statements about vertical and linear pairs.

Explanation

Vertical angles are equal and opposite. Linear pairs share a side and form 180°. However, only linear pairs sum to 180°, not vertical angles.

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18) If ∠A = (4x − 20)° and its vertical angle is (2x + 20)°, find ∠A.

Explanation

Equate: 4x − 20 = 2x + 20 ⇒ 2x = 40 ⇒ x = 20. Substitute: ∠A = 4(20) − 20 = 60°.

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19) If ∠1 = 100° and ∠2 = 80°, what is true about the pair?

Explanation

100° + 80° = 180°, so they form a linear pair (supplementary), not vertical.

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20) If ∠x = (5y − 25)° and its vertical angle = (3y + 15)°, find y = __.

Explanation

Set equal: 5y − 25 = 3y + 15 ⇒ 2y = 40 ⇒ y = 20. Each angle = 5(20) − 25 = 75°.

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If ∠A = 70°, what is the measure of its vertical angle?
Select all true statements about vertical angles.
The sum of all four angles formed by two intersecting lines is 360°.
If one angle in an intersection is 110°, what is its vertical angle?
All pairs of vertical angles are congruent.
Two lines intersect forming one 130° angle. What is the measure of...
Vertical angles can be both acute and obtuse at the same intersection.
Vertical angles are always supplementary.
Two lines intersect forming one angle of 120°. The vertical angle...
If ∠1 = 3x + 10 and ∠2 = 5x − 30, and the angles are...
If one of two vertical angles measures 85°, what is the other angle?
If ∠x = 2x + 20 and its vertical angle is 5x − 40, find x =...
Two vertical angles are (4y − 5)° and (3y + 10)°. Find the measure...
If one angle at an intersection is 45°, then the opposite vertical...
Two lines intersect. If ∠1 = 3x + 12 and ∠2 = 2x + 32 are...
In a diagram, ∠A = 60°. What is the measure of its supplementary...
Select all correct statements about vertical and linear pairs.
If ∠A = (4x − 20)° and its vertical angle is (2x + 20)°, find...
If ∠1 = 100° and ∠2 = 80°, what is true about the pair?
If ∠x = (5y − 25)° and its vertical angle = (3y + 15)°, find y =...
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