Angle Relationships: Straight, Intersecting & Perpendicular Lines

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 8 · Geometry of Straight Lines

MARKING GUIDELINE

Marks

Duration

1 hour

Questions

Name:

Class:

Date:

Mark

/ 37

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
Angles on a straight line add up to …
(1)
A)360°
B)270°
C)90°
D)180°✓
Answer: D — A straight line is half a full turn.
- A — that is angles round a POINT
- B — that is three right angles
- C — that is a right angle
1.2
Angles round a point add up to …
(1)
A)360°✓
B)540°
C)90°
D)180°
Answer: A — A full turn is 360°.
- B — that is the angle sum of a pentagon
- C — that is a right angle
- D — that is angles on a straight line
1.3
Two lines intersect. One angle is 65°. The angle VERTICALLY OPPOSITE it is …
(1)
A)295°
B)65°✓
C)115°
D)25°
Answer: B — Vertically opposite angles are EQUAL.
- A — that is the reflex angle
- C — that is the adjacent angle on the straight line
- D — that is the complement
1.4
Two angles on a straight line are x and 3x. The value of x is …
(1)
A)45°✓
B)30°
C)60°
D)90°
Answer: A — x + 3x = 180°, so 4x = 180°.
- B — divided 180 by 6
- C — divided 180 by 3
- D — divided 180 by 2
1.5
Two angles that add up to 90° are called …
(1)
A)adjacent
B)complementary✓
C)supplementary
D)vertically opposite
Answer: B — Complementary angles complete a right angle.
- A — adjacent only means next to each other
- C — supplementary angles add to 180°
- D — those are equal, not adding to 90°
1.6
Perpendicular lines meet at …
(1)
A)90°✓
B)45°
C)180°
D)360°
Answer: A — Perpendicular means at right angles.
- B — that is half a right angle
- C — that is a straight line
- D — that is a full turn
1.7
An angle of 130° is called …
(1)
A)reflex
B)acute
C)obtuse✓
D)right
Answer: C — An obtuse angle is between 90° and 180°.
- A — reflex is more than 180°
- B — acute is less than 90°
- D — a right angle is exactly 90°
1.8
The SUPPLEMENT of 47° is …
(1)
A)47°
B)313°
C)43°
D)133°✓
Answer: D — 180° − 47° = 133°.
- A — supplementary angles are not equal
- B — that is the reflex angle
- C — that is the COMPLEMENT
1.9
Three angles round a point are 90°, 130° and x. Then x is …
(1)
A)220°
B)140°✓
C)360°
D)40°
Answer: B — 360° − 90° − 130° = 140°.
- A — added the two given angles
- C — forgot to subtract at all
- D — used 180° instead of 360°
1.10
Which statement about vertically opposite angles is TRUE?
(1)
A)they add up to 180°
B)they are always acute
C)they are equal✓
D)they add up to 90°
Answer: C — When two lines cross, the angles opposite each other are equal.
- A — that is true of angles on a straight line
- B — they can be any size
- D — that is complementary angles

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, two straight lines intersect at O. The diagram is not drawn to scale.

2.1
Calculate the value of x.
(3)
(3x + 10)° = (5x − 30)° (vertically opposite angles) (1)
40 = 2x (1)
x = 20 (1)
2.2
Hence determine the size of the angle marked (3x + 10)°.
(3)
= 3(20) + 10 (1)
= 60 + 10 (1)
= 70° (1)
2.3
Hence determine, with a reason, the size of y.
(4)
y = 180° − 70° (angles on a straight line) (2)
= 110° (1)
(check: 70° + 110° = 180°) (1)

Question 3

[9 MARKS]

Four rays meet at the point O in the diagram below. The diagram is not drawn to scale.

3.1
Write down an equation in x and solve it.
(4)
2x + 3x + (x + 30°) + 90° = 360° (angles round a point) (2)
6x + 120° = 360° (1)
x = 40° (1)
3.2
Hence write down the size of each of the three unknown angles.
(3)
2x = 80° (1)
3x = 120° (1)
x + 30° = 70° (1)
3.3
Show that your four angles are correct.
(2)
80° + 120° + 70° + 90° (1)
= 360°, the angles round a point (1)

Question 4

[8 MARKS]

Answer the following. Show all your working.

4.1
Two angles, (2y − 10)° and (y + 40)°, are complementary. Calculate the value of y and the size of each angle.
(4)
(2y − 10) + (y + 40) = 90 (complementary angles add to 90°) (1)
3y + 30 = 90 (1)
y = 20 (1)
The angles are 30° and 60° (1)
4.2
An angle is three times the size of its supplement. Calculate the size of the angle.
(4)
Let the angle be x, so its supplement is (180° − x) (1)
x = 3(180° − x) (1)
x = 540° − 3x, so 4x = 540° (1)
x = 135° (check: 3 × 45° = 135°) (1)

TOTAL: 37 marks

This question paper consists of 4 questions.