Angles in Triangles and Quadrilaterals: Full Guide — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 8–9 · Geometry

Angles in Triangles and Quadrilaterals: Full Guide

EXAM-STYLE CLASS TEST

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
The angles of a triangle add up to …
(1)
A)90°
B)180°
C)360°
D)540°
1.2
The angles of a quadrilateral add up to …
(1)
A)180°
B)360°
C)270°
D)540°
1.3
Two angles of a triangle are 55° and 65°. The third is …
(1)
A)120°
B)60°
C)240°
D)70°
1.4
A triangle with all three sides equal is called …
(1)
A)isosceles
B)equilateral
C)scalene
D)right-angled
1.5
The base angles of an ISOSCELES triangle are …
(1)
A)always 60°
B)equal to each other
C)always right angles
D)always different
1.6
The EXTERIOR angle of a triangle equals …
(1)
A)the adjacent interior angle
B)the sum of the two opposite interior angles
C)180°
D)the largest interior angle
1.7
Which quadrilateral has diagonals that bisect each other AT RIGHT ANGLES but are NOT equal?
(1)
A)rectangle
B)rhombus
C)square
D)trapezium
1.8
Opposite angles of a PARALLELOGRAM are …
(1)
A)supplementary
B)equal
C)complementary
D)right angles
1.9
Three angles of a quadrilateral are 80°, 95° and 110°. The fourth is …
(1)
A)75°
B)85°
C)285°
D)95°
1.10
Every square is a rectangle because …
(1)
A)all its sides are equal
B)it has four right angles
C)its diagonals are equal
D)it is a quadrilateral

Answer grid — circle your answers for Question 1

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 △ABC below the three interior angles are given as x, 2x and 3x. The diagram is not drawn to scale.

2.1
Calculate the value of x.
(3)
2.2
Hence write down the size of each angle, and state what kind of triangle ABC is. Give a reason.
(4)
2.3
In a different triangle the three angles are equal. Determine the size of each angle and name the triangle.
(3)

Question 3

[7 MARKS]

In the diagram below, one side of the triangle has been produced to form the exterior angle y. The diagram is not drawn to scale.

3.1
Determine, with a reason, the size of y.
(3)
3.2
Hence determine the size of the third interior angle of the triangle, in two different ways.
(4)

Question 4

[10 MARKS]

Answer the following questions about quadrilaterals.

4.1
The four angles of a quadrilateral are x, (x + 20)°, 2x and (2x + 40)°. Calculate the value of x.
(3)
4.2
Hence write down the sizes of the four angles and check your answer.
(3)
4.3
ABCD is a parallelogram with Â = 70°. Determine, with reasons, the sizes of B̂ and Ĉ.
(4)

TOTAL: 37 marks

This question paper consists of 4 questions.

Statement	Reason

Statement	Reason

Statement	Reason

Statement	Reason