📐 Geometry · Basics
Angle Relationships: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
Vertical angles formed by two crossing lines have equal measures.
✓ True. Each vertical angle is a linear pair with the same neighbor, so each equals 180° minus that neighbor. That makes them equal.
Adjacent angles are always supplementary.
✗ False. Adjacent angles can add to any amount. Adjacent angles of 15° and 40° add to 55°. They are supplementary only when their outer sides form a straight line.
The two angles of a linear pair always add to 180°.
✓ True. A linear pair makes a straight line, and a straight angle measures 180°.
Two supplementary angles must share a side.
✗ False. Supplementary only describes the sum. A 116° angle in one place and a 64° angle in another are supplementary without touching.
Angles measuring 25° and 65° are complementary, even if they are far apart in a drawing.
✓ True. 25° + 65° = 90°. Complementary angles do not have to be adjacent.
If two angles in a diagram look equal, you can assume they are equal.
✗ False. Diagrams are not drawn to scale unless marked. Only given measures and equal-angle marks tell you two angles are equal.
The complement of an angle measuring x° is (90 − x)°, as long as 0 < x < 90.
✓ True. The two measures must add to 90°, so the partner is 90 − x. It is a real angle only when x is between 0 and 90.
An obtuse angle can have a complement.
✗ False. An obtuse angle measures more than 90°, so 90 − x would be negative, and an angle cannot be negative.
If ray BD bisects ∠ABC and m∠ABC = 130°, then m∠ABD = 65°.
✓ True. A bisector makes two equal halves, and 130° ÷ 2 = 65°.
Angles that fill the space around a point add up to 180°.
✗ False. A full turn around a point is 360°. The number 180° is for a straight angle, which is half a turn.
Two crossing lines form two pairs of vertical angles.
✓ True. The four angles at a crossing make two pairs of opposite angles, and each pair is equal.
Vertical angles are always supplementary.
✗ False. Vertical angles are equal. They would be supplementary only if each measured 90° (equal angles that add to 180° must each be 90°). In general, it is the neighbors that add to 180°.
If (2x + 6)° and (5x − 24)° are vertical angles, then x = 10.
✓ True. Vertical angles are equal: 2x + 6 = 5x − 24 gives 30 = 3x, so x = 10. Check: 2(10) + 6 = 26 and 5(10) − 24 = 26.
A 90° angle is supplementary to an acute angle.
✗ False. The supplement of 90° is 180° − 90° = 90°, a right angle, which is not acute.