Constructing angles of 90° and 45° | Maths | Quizalize & Oak National Academy

Starter quiz

Andeep constructs the bisector of an angle of 104°. Andeep has made angles of ______°.

'52' ✓
The diagram shows two congruent isosceles triangles put together to form a rhombus. Match each angle to its size.

$a$ °

⇔

32° ✓

$b$ °

⇔

64° ✓

$c$ °

⇔

116° ✓

Not a marked angle

⇔

44° ✓
Here are the steps to construct a rhombus given the legs of an angle. Match each step to the correct instruction.

Step 1

⇔

Set your compasses to a width equal to the shorter of the two legs. ✓

Step 2

⇔

Place your compass needle on the vertex of the angle. ✓

Step 3

⇔

Make an arc on each leg, then place the compass needle on one arc. ✓

Step 4

⇔

Place the pencil on the vertex of the angle. Draw a circle. ✓

Step 5

⇔

Repeat on the open endpoint of the other leg. ✓

Step 6

⇔

Draw lines with a ruler to connect the points to form a rhombus. ✓
Jacob wants to construct a rhombus using an angle with leg lengths of 10 cm and 15 cm. The maximum radius of each circle in the construction of this rhombus is ______ cm.

'10' ✓
Lucas begins construction of a rhombus from this angle. Which point is the final vertex of the rhombus?

A

B ✓

C

D
Jun is constructing an angle bisector. Here are the construction marks. Which two arcs did Jun draw first?

a ✓

b

c ✓

d

Complementary angles are a pair of angles that sum to ______°.

'90' ✓
The diagram shows the perpendicular to UV that passes through the point T. The perpendicular intersects UV at point S. Which of these constructions will produce a 45° angle?

The perpendicular bisector of ST.

The perpendicular bisector of TV.

The angle bisector of UST. ✓

The angle bisector of UTV

The angle bisector of TSV. ✓
EC is a perpendicular to BD. The angle BOE is bisected. Match each angle to its size.

Angle BOC

⇔

90° ✓

Angle AOE

⇔

45° ✓

Angle AOD

⇔

135° ✓

Reflex angle AOE

⇔

315° ✓

Reflex angle AOD

⇔

225° ✓
The line segments AB and BC form an angle of 110°. Which of these constructions creates a 55° angle?

The perpendicular bisector of BC.

A perpendicular to AB through B.

An extension of AB in the direction of B.

An angle bisector of the angle ABC. ✓
Line segments AB and BC are the legs of a 124° angle. The diagram shows the two constructions that are applied to ABC. The angle $x$ ° is ______°.

'28' ✓
Line segments AB and BC are the legs of a 124° angle. The diagram shows the two constructions that are applied to ABC. The angle $z$ ° is ______°.

'118' ✓

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Pupils may use a protractor rather than a pair of compasses.

Remind pupils that a construction is done using a pair of compasses and ruler.

Bisect - To bisect means to cut or divide an object into two equal parts.
Complementary angles - Complementary angles are a pair of angles that sum to 90°.
Supplementary angles - Supplementary angles are a pair of angles that sum to 180°.
Conjugate angles - Conjugate angles are a pair of angles that sum to 360°.