Vertical Angles Quiz: Master Vertical Angles Quiz

Vertical angles are always congruent. The angle directly opposite a 45° angle also measures 45°. Option A gives 135° = 180° - 45°, the supplement not the vertical angle. Option B gives 90°, which applies only to perpendicular intersections. Option C gives 55°, which has no relationship to 45° in this context.

The answer is True. When two lines intersect at an angle other than 90°, one pair of vertical angles is acute and the other pair is obtuse. For example, if one angle is 60°, its vertical angle is also 60° (acute), while the two adjacent angles are each 120° (obtuse). The two pairs of vertical angles at any non-perpendicular intersection are always one acute pair and one obtuse pair.

Set equal: 5y - 25 = 3y + 15. Subtract 3y: 2y - 25 = 15. Add 25: 2y = 40, so y = 20. Check: 5(20)-25 = 75° and 3(20)+15 = 75°, confirming equality. Option A gives y=10: 25 and 45, not equal. Option B gives y=15: 50 and 60, not equal. Option D gives y=25: 100 and 90, not equal.

100° + 80° = 180°, so the angles are supplementary. They form a linear pair. Option A is false because vertical angles must be equal, but 100° ≠ 80°. Option B is false because complementary angles sum to 90°, not 180°. Option D is false because they are not equal and the description is contradictory.

Vertical angles are congruent, so the angle directly opposite also measures 130°. Option A gives 50° = 180° - 130°, which is the supplement — this is the adjacent angle forming a linear pair, not the vertical angle. Options C and D have no direct geometric relationship to 130° in this context.

Set equal: 4x - 20 = 2x + 20. Subtract 2x: 2x - 20 = 20. Add 20: 2x = 40, so x = 20. Substitute: angle A = 4(20) - 20 = 80 - 20 = 60°. Check: 2(20)+20 = 60°, confirming equality. Option A gives 40°, requiring x=15: 4(15)-20=40 but 2(15)+20=50, not equal.

Vertical angles are always congruent, confirming A. Linear pairs are adjacent angles on a straight line and always sum to 180°, confirming B. Vertical angles share the intersection point as their vertex but have no side in common, confirming C. Option D is false — only linear pairs always sum to 180°. Vertical angles sum to 180° only in the special case where both measure 90°, not in general.

Supplementary angles sum to 180°. So the supplement of 60° = 180° - 60° = 120°. Option A gives 60°, which would be the vertical angle or an equal angle, not the supplement. Option B gives 90°, which is the complement of 60°, not the supplement. Option D gives 180°, the total sum, not one of the angles.

The answer is True. By the vertical angles theorem, whenever two lines intersect, the two pairs of opposite angles formed are always congruent. This holds regardless of the angle measures — whether the angles are acute, right, or obtuse. The congruence of vertical angles is a fundamental theorem in geometry with no exceptions.

Set equal: 3x + 12 = 2x + 32. Subtract 2x: x + 12 = 32. Subtract 12: x = 20. Check: 3(20)+12 = 72° and 2(20)+32 = 72°, confirming equality. Option A gives x=8: 36 and 48, not equal. Option B gives x=10: 42 and 52, not equal. Option C gives x=12: 48 and 56, not equal.

When two lines intersect, vertical angles are the opposite pair and are always congruent. If angle A = 70°, its vertical angle also measures 70°. Option B gives 90°, which would only be true if the lines were perpendicular. Option C gives 110° = 180° - 70°, which is the supplementary angle not the vertical angle. Option D gives the sum of all angles around a point.

Vertical angles are congruent, so the angle directly opposite also measures 110°. Option A gives 70° = 180° - 110°, which is the supplement — this is the adjacent angle in the linear pair, not the vertical angle. Option B gives 90°, true only for perpendicular lines. Option D gives 130°, which has no direct relationship to 110° in this context.

The answer is True. Two intersecting lines form four angles around the intersection point. A complete rotation around any point always equals 360°. The four angles consist of two pairs of vertical angles. If one angle is x°, its vertical angle is also x°, and the two adjacent angles are each (180° - x°). Adding all four: x + x + (180°-x) + (180°-x) = 360°.

Set equal: 4y - 5 = 3y + 10, giving y = 15. Substitute: 4(15) - 5 = 60 - 5 = 55°. Check: 3(15) + 10 = 45 + 10 = 55°, confirming both angles are 55°. Option A gives 35°, requiring y = 10: 4(10)-5=35 but 3(10)+10=40, not equal. Option B gives 40° and option C gives 45°, both failing the equality check.

Vertical angles are congruent: 2x + 20 = 5x - 40. Subtract 2x: 20 = 3x - 40. Add 40: 60 = 3x, so x = 20. Check: 2(20)+20 = 60° and 5(20)-40 = 60°, confirming equality. Option A gives x=10: 2(10)+20=40 and 5(10)-40=10, not equal. Option B gives x=15: 50 and 35, not equal. Option D gives x=25: 70 and 85, not equal.

Vertical angles are always equal in measure, confirming A. They are positioned directly opposite each other at the intersection point, confirming B. They are created specifically when two straight lines cross, confirming D. Option C is false — vertical angles do not share a common side. Angles that share a common side are called adjacent angles, which is a different relationship entirely.

Vertical angles are always congruent. Both angles in a vertical pair have identical measures, so the other angle also measures 85°. Option B gives 95° = 180° - 85°, which is the supplement. Option C gives 100°, which has no relationship to 85°. Option D gives 180°, the sum of supplementary angles.

Vertical angles are congruent, so set them equal: 3x + 10 = 5x - 30. Subtract 3x from both sides: 10 = 2x - 30. Add 30: 40 = 2x, so x = 20. Check: 3(20)+10 = 70° and 5(20)-30 = 70°, confirming equality. Options A, B, and C all fail this verification check.

Vertical angles are opposite angles formed by two intersecting lines and are always congruent. If one angle measures 120°, the angle directly across from it also measures 120°. Option A gives 60° = 180° - 120°, which is the supplement, not the vertical angle. Options B and C have no direct relationship to the given angle.

The answer is False. Vertical angles are congruent — they are equal in measure, not supplementary. Supplementary angles sum to 180°. Two vertical angles only sum to 180° in the special case where each measures exactly 90°, which happens only when the intersecting lines are perpendicular. In general, vertical angles are equal, not supplementary.