Angles on Parallel Lines: The Complete Exam Guide — Worksheet & Memo

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Grade 8–9 · Geometry

Angles on Parallel Lines: The Complete Exam Guide

MARKING GUIDELINE

Marks

Duration

45 minutes

Questions

Name:

Class:

Date:

Mark

/ 29

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
When two parallel lines are cut by a transversal, CO-INTERIOR angles are …
(1)
A)equal
B)SUPPLEMENTARY✓
C)complementary
D)vertically opposite
Answer: B — Co-interior (allied) angles add up to 180°.
- A — that is true of alternate and corresponding angles
- C — they add to 180°, not 90°
- D — vertically opposite angles are formed by crossing lines
1.2
ALTERNATE angles between parallel lines are …
(1)
A)supplementary
B)equal✓
C)complementary
D)always right angles
Answer: B — They lie on opposite sides of the transversal and are equal.
- A — that is co-interior angles
- C — they add to 180° only if each is 90°
- D — they can be any size
1.3
CORRESPONDING angles between parallel lines are …
(1)
A)supplementary
B)equal✓
C)complementary
D)unequal
Answer: B — They sit in matching positions at the two intersections.
- A — that is co-interior angles
- C — they would add to 90°, which happens only if both are 45°
- D — equal is precisely what they are
1.4
Two parallel lines are cut by a transversal. One co-interior angle is 110°. The other is …
(1)
A)110°
B)70°✓
C)250°
D)20°
Answer: B — 180° − 110° = 70°.
- A — treated co-interior angles as EQUAL — that is alternate angles
- C — used 360°
- D — used 90°
1.5
Lines AB and CD are parallel. An alternate angle to one of 63° is …
(1)
A)117°
B)63°✓
C)27°
D)297°
Answer: B — Alternate angles are EQUAL.
- A — that is the co-interior angle
- C — that is the complement
- D — that is the reflex angle
1.6
Which pair of angles proves that two lines are PARALLEL?
(1)
A)two angles that add to 90°
B)equal corresponding angles✓
C)two angles on a straight line
D)vertically opposite angles
Answer: B — Equal corresponding angles is the converse test for parallel lines.
- A — complementary angles say nothing about parallel lines
- C — that is true whether or not the lines are parallel
- D — those are equal at ANY crossing
1.7
In the letter Z between parallel lines, the two angles are …
(1)
A)co-interior
B)alternate and EQUAL✓
C)corresponding
D)supplementary
Answer: B — The Z shape is the classic picture of alternate angles.
- A — co-interior angles make a C or U shape
- C — corresponding angles make an F shape
- D — alternate angles are equal, not supplementary
1.8
Two parallel lines are cut by a transversal. If one angle is 90°, then …
(1)
A)only that angle is 90°
B)ALL eight angles are 90°✓
C)four are 90° and four are 180°
D)the lines are not really parallel
Answer: B — Every angle is either equal to it or supplementary to it, and 180° − 90° = 90°.
- A — equal and supplementary angles are all 90° here
- C — no angle at a crossing is 180°
- D — a perpendicular transversal is perfectly possible
1.9
Angles of x and (2x + 30)° are co-interior between parallel lines. Then x = …
(1)
A)70°
B)50°✓
C)30°
D)60°
Answer: B — x + 2x + 30 = 180 gives 3x = 150.
- A — used 210 instead of 150
- C — divided 90 by 3
- D — divided 180 by 3
1.10
Which statement is TRUE for lines that are NOT parallel?
(1)
A)alternate angles are still equal
B)alternate angles need NOT be equal✓
C)corresponding angles are still equal
D)co-interior angles still add to 180°
Answer: B — All three of those properties require the lines to be parallel.
- A — that needs parallel lines
- C — that needs parallel lines
- D — that needs parallel lines

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[10 MARKS]

In the diagram below, AB ∥ CD and a transversal cuts both lines. One angle of 64° is given. Determine, with a reason, the size of EACH of the angles a, b and c. The diagram is not drawn to scale.

2.1
The size of a.
(3)
a = 64° (1)
corresponding angles (1)
AB ∥ CD (1)
2.2
The size of b.
(3)
b = 180° − 64° (1)
= 116° (1)
angles on a straight line (1)
2.3
The size of c.
(4)
c = a (1)
vertically opposite angles (1)
= 64° (1)
(check: b + c = 116° + 64° = 180°) (1)

Question 3

[9 MARKS]

Answer the following.

3.1
Two co-interior angles between a pair of parallel lines are (2x + 20)° and (3x − 10)°. Calculate the value of x.
(3)
(2x + 20) + (3x − 10) = 180 (co-interior angles are supplementary) (1)
5x + 10 = 180 (1)
x = 34 (1)
3.2
Hence determine the size of each of the two angles, and check your answer.
(3)
2(34) + 20 = 88° (1)
3(34) − 10 = 92° (1)
88° + 92° = 180° ✓ (1)
3.3
Two straight lines are cut by a transversal. A pair of alternate angles are both 75°. State, with a reason, whether the two lines are parallel.
(3)
Yes, the lines are parallel (1)
The alternate angles are equal (1)
(converse: if alternate angles are equal the lines are parallel) (1)

TOTAL: 29 marks

This question paper consists of 3 questions.