Angles in 2D Shapes FSQ1
Calculate the missing angles in the following 2D shapes.
Angles in 2D Shapes FS1(a)
Calculate the angle marked x in the quadrilateral below
Answer type: simple
Answer: 92 \degree
Workings:
x=360-95-123-50=92\degree1 mark
Angles in 2D Shapes FS1(b)
Calculate the angle marked a in the following triangle
Answer type: simple
Answer: 89 \degree
Workings:
x=180-56-35=89\degree1 mark
Angles in 2D Shapes FS1(c)
Calculate the missing angle p in the following quadrilateral
Answer type: simple
Answer: 125 \degree
Workings:
x=360-102-75-58=125\degree1 mark
Angles in 2D Shapes FSQ2
The diagram below shows the side view of a house.
Calculate the angle in the roof.
Answer type: simple
Answer: 96 \degree
Workings:
The side lengths of the triangle which form the roof are equal, so the triangle is isosceles – the base angles are also equal.
x = 180-42-42=96\degreeAngles in 2D Shapes FSQ3
A window cleaner positions a ladder alongside a rectangular building on level ground, as shown in the following diagram.
Calculate the angle between the floor and the ladder, assuming that the building is vertically upright.
Answer type: simple
Answer: 60 \degree
Workings:
The building is upright and the ground is level, so the angle between the building and the ground is 90\degree
Therefore, x=180-90-30=60
1 mark
Angles in 2D Shapes FSQ4
Consider the following 2D shapes.
Angles in 2D Shapes FS4(a)
The diagram below shows a regular hexagon divided into 6 equal triangles.
Calculate the angle marked a
Answer type: simple
Answer: 60 \degree
Workings:
The angles around a single point add up to 360\degree
So a=360\div 6=60\degree
1 mark
Angles in 2D Shapes FS4(b)
The following diagram shows a regular pentagon divided into 10 equal triangles.
Calculate the angle marked b
Answer type: simple
Answer: 36 \degree
Workings:
The angles around a single point add up to 360\degree
So b=360\div 10=36\degree
1 mark
Angles in 2D Shapes FSQ5
ABCD is a rectangle.
Calculate the angle x
Answer type: simple
Answer: 72 \degree
Workings:
To work out x, the other two angles in the triangle need to be calculated.
The missing angles can be calculated as follows:
180-121=59\degree (angles on a straight line add up to 180\degree)
90-41=49 (the corner of a rectangle is a right-angle)
The angle x=180-59-49=72 \degree[/latex] (angles in a triangle add up to 180\degree
3 marks
Angles in 2D Shapes FSQ6
The diagram below shows a rectangular garden featuring a square patch of grass.
Angles in 2D Shapes FS5(a)
Calculate the angle marked m
Answer type: simple
Answer: 53 \degree
Workings:
The angles in a triangle add up to 180\degree
The decking is a right-angled triangle, so
m=180-90-37=53\degree1 mark
Angles in 2D Shapes FS5(b)
Calculate the angle marked n
Answer type: simple
Answer: 127 \degree
Workings:
The pond is a trapezium, which has 4 sides, so the internal angles add up to 360\degree
The top left corner can be calculated as follows:
90-37=53The two angles next to the grass are right-angles, as the grass is square and the garden forms a rectangle.
So the angle n can be calculated as follows:
n=360-90-90-53=1273 marks