AUTHOR EVERYTHING YOU NEED TO KNOW TO GET A GRADE C GEOMETRY & MEASURES (FOUNDATION)
Jan 02, 2016
110°
Base angles in a kite are equal
Opposite angles in a rhombus are equal
250°
Angles around a point sum to 360°
Angles in a kite sum to 360°
30
Replace a with 3 and b with 5.2 P = 2 x 3 + 2 x 5.2P = 6 + 10.4
16.4
Total areas of both shapes are equal to one as shown.
9cm
5cm 5cm
5cm
3cm 3cm Can choose either as your answer
Any two of rectangle, parallelogram, kite or arrowhead
The 3cm and 5cm rods would not meet when joined with the 9cm rod.
In an isosceles triangle, the base angles are the same
Angles in a triangle sum to
180°
80 20
50 50
Each angle is 60° in an equilateral triangle
120° because angles on a straight line add to 180°30° because angles in a right angle add to 90°
Base angles are both 30° so ABD is an isosceles triangle
Isosceles TriangleAngles in a triangle
add to 180°
180° - 34° = 146° 146° ÷ 2 = 73°
73
73°
73°
107°
107° because angles on a straight line add up to 180°
y = 180° - 107° - 38° = 35°
35
35°
No, because 38° is not equal to 35°. Therefore, it is not an isosceles triangle
180° - 126° = 54° 54° ÷ 2 = 27°
27° 27° 153°
153° because angles on a straight line add up to 180°
Angles in a triangle add to 180°
27 153
Base angles are the same in an isosceles triangle
80°
Angles in a triangle add to 180°180° - 80° - 80° = 20°
20
Means work out angle A in triangle ABC
Means work out angle R in triangle PQR
Base angles are the same in an isosceles triangle
70°
Angles in a triangle add to 180°180° - 70° - 70° = 40°
40°
A right angle is 90°90° - 40° = 50°
50°
Both base angles are equal180° - 50° = 130° 130° ÷ 2 = 65°
65°65°
65
180° - 48° = 132° 132° ÷ 2 = 66°
66° 66°
Angles on a straight line add to 180°180° - 66° = 114°
114°
114
A quadrilateral is made up of two triangles Angles is a triangle add up to 180°
180°
180° 180° + 180° = 360°
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(because the exterior angles add up to 360°)
Exterior angle = 72°
72°
Two exterior angles joined
togetherAs worked out in part (a)
72°
144
All the angles and sides are the same in a regular pentagon
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Exterior angle
Exterior angle
Exterior angle
Exterior angle
Exterior angle
= 72°
72°
72°
72°
72°
72°
Interior angle
Angles on a straight line add up 180° Interior angle = 180° - 72° = 108°
108°
Base angles in a isosceles triangle are the same 180° - 108° = 72°
36°
36°
36
LEARN OFF BY HEARTInterior angle
Exterior angle
Angles on a straight line add up 180°
Exterior angle = 180° - 162° = 18°
= 20 20
Decagon Pentagon
Interior angle
Sum of interior angles of an decagon = (10 – 2) x 180°
Sum of interior angles = (number of sides – 2) x 180°
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= 8 x 180° = 1440°
= 144°
144°Interior angle
Sum of interior angles of a pentagon = (5 – 2) x 180° = 3 x 180° = 540°
= 108°
108°
Angles around a point add up to 360°
360° - 144° - 108° = 108°
108°
Base angles in a isosceles triangle are the same
180° - 108° = 72° 72° ÷ 2 = 36°
36°36°
144°
144° + 36° = 180° (Angles on a straight line add up to 180°) Therefore, ABC lie on a straight line
Hexagon
Square
Square
Sum of interior angles = (number of sides – 2) x 180°
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Sum of interior angles of an hexagon = (6 – 2) x 180° = 4 x 180° = 720°
= 120°
Interior angle120°
Angles around a point add up to 360°
360° - 120° - 90° - 90° = 60°
60°
Base angles are the same
180° - 60° = 120° 120° ÷ 2 = 60°
60°60°
Therefore, as all angles are 60° AHJ is equilateral
Sum of interior angles = (number of sides – 2) x 180°
LEARN OFF BY HEARTSum of interior angles of an octagon = (8 – 2) x 180° = 6 x 180° = 1080°
= 135°
135
= 135° As worked out in part (a)
135°
135°135°
135° 135°135°
135°135°
Angles around a point add up to 360°
360° - 135° - 135° = 90°
Therefore, as all angles are 90° PQRS is a square