Straight lines, crossings, and vertically opposite angles

Mathematics · Geometry · ages 11-13

Name ______________________ Date ____________

Two straight lines cross. A pair of vertically opposite angles has measures 2x degrees and 64 degrees. What is x?
Answer: ______________
Which pair of positive angles can exactly fill a straight angle with no gaps or overlaps?
- 70° and 110°
- 80° and 110°
- 90° and 100°
Two angles lie on a straight line, exactly filling it with no gaps or overlaps. One is 65°. What is the other angle?
- 115°
- 65°
- 295°
When two straight lines cross, the four non-reflex angles made always add up to 360°.
Circle one: True False
A straight angle is split into two adjacent angles that exactly fill it: one is 40 degrees and the other is (2x + 20) degrees. What is x?
Answer: ______________
Two straight lines cross at a point. Two of the vertically opposite angles are each 25°. What is the size of one of the other two angles at that point?
Answer: ______________
Two straight lines cross. One pair of vertically opposite angles is marked (2x + 10)° and (x + 55)°. Which equation expresses their equality?
- 2x + 10 = 180
- 2x + 10 = x + 55
- x + 55 = 90
Two positive vertically opposite angles can be in the ratio 2:1.
Circle one: True False
Two lines cross. One angle is 118°. Find the angle next to it on the straight line, then find the angle vertically opposite that new angle. What is the final angle?
- 242°
- 62°
- 118°
Two straight lines cross. One pair of vertically opposite angles is marked (3x)° and (x + 40)°. A neighbouring angle is split into two equal parts. What is each part?
- 60°
- 120°
- 30°

Answer key

For grown-ups. Fold this page away before handing over the rest.

Straight lines, crossings, and vertically opposite angles W1-mt_tedML_iu4Y-s1

32 · Vertically opposite angles are equal, so 2x = 64. Divide by 2: x = 32.
70° and 110° · 70 + 110 = 180, so that pair exactly fills a straight angle. 80 + 110 = 190 and 90 + 100 = 190, so those pairs overshoot.
115° · Angles exactly filling a straight angle add to 180°, so the missing angle is 180° - 65° = 115°.
True · The four non-reflex openings fill one full turn around the crossing point with no gaps or overlaps, and a full turn is 360°.
60 · The two angles exactly fill a straight angle, so 40 + (2x + 20) = 180. Simplify: 2x + 60 = 180. Subtract 60: 2x = 120. Divide by 2: x = 60.
155 · Each 25° angle sits on a straight angle with one of the other angles, so that angle is 180 - 25 = 155°.
2x + 10 = x + 55 · Vertically opposite angles are equal, so set the two expressions equal: 2x + 10 = x + 55.
False · Vertically opposite angles are equal, so their ratio is always 1:1. A 2:1 ratio is impossible.
62° · The angle next to 118° on the straight angle is 180 - 118 = 62°. The angle vertically opposite that 62° angle is also 62°.
60° · Set the opposite pair equal: 3x = x + 40. Subtract x: 2x = 40. Divide by 2: x = 20. Each opposite angle is 3(20) = 60°. The neighbour is 180 - 60 = 120°. Split equally: 120 / 2 = 60°.