Polygons and naming figures
Angle sum of a triangle
Types of triangles
Exterior angle theorem
Quadrilaterals
100
Is a circle a polygon? Explain why or why not.
No. A polygon must have only straight sides; a circle has a curved edge.
100
Find the missing angle?
180 − 82 − 55 = 43
100
Name a triangle that has all sides equal?
Equilateral (and all angles are 60°).
100
Fill in the blank:
An exterior angle is created by (1)......... one side of a triangle.
An exterior angle of a triangle equals the (2)........ of its two interior (3).......... angles.
(1) extending
(2) sum
(3) opposite
100
True or false? The interior angle sum of a quadrilateral is 180 degrees? If false, how would you correct this statement.
False. The interior angle sum of a quadrilateral is 360 degrees.
200
What is the name of a 9-sided polygon?
Nonagon
200
A right-angled triangle has an angle of 40°. Find the other acute angle. Justify your answer.
180 - 90 - 40 = 50 (Angle Sum of a Triangle)
200
Classify the following triangle and justify your answer
Obtuse-angled Triangle (it has one angle > 90 degrees)
200
Find x? Give reasons
x = 64 + 45 (Exterior Angle Theorem)
x = 109
200
Evaluate the missing angle?
Missing angle = 360 - 112 - 78 - 76
Missing angle = 94 (Angle Sum of a Quad)
300
How many sides does a decagon have?
10
300
Find the value of x? Give reasons
(x + 12) + 30 + 42 = 180 (Angle Sum of a Triangle)
x + 84 = 180
x = 180 - 84
x = 96
300
Name the following triangle by its angles
Right-angled Isosceles Triangle
300
Find p? Show all necessary workings
180 - 110 = 70 (Straight angle / supplementary)
p = 130 - 70 (Exterior Angle Theorem)
p = 60
300
I am a quadrilateral whose diagonals bisect each other and are equal in length. Who am I?
Rectangle
Square
400
State whether each is regular or irregular:
square, rectangle.
Give the reasons
Square is regular (all sides equal);
Rectangle is irregular (sides can be unequal).
400
Find the value of the pronumeral?
(5x + 5) + (2x + 1) + 90 = 180 (Angle Sum of a Triangle)
⇒7x + 96 = 180
⇒ 7x = 84
⇒ x = 12∘
400
Can an equilateral triangle be an isosceles triangle? Explain why?
Yes, an equilateral triangle can be an isosceles triangle because an isosceles triangle is defined as having at least two equal sides, while an equilateral triangle has three equal sides.
400
Evaluate the value of x?
20x = 60 + (7x + 5) (Exterior Angle Theorem)
20x - 7x = 60 + 5
13x = 65
x = 5
400
I am a quadrilateral.
I have two pairs of adjacent sides equal.
My adjacent sides are not perpendicular.
Who I am? Name all possible answers to get the point
Kite and Rhombus
500
A polygon has interior angle sum 1620°. What is it called?
Hint: Angle sum of a 2D shape = (n - 2) x 180
n is the number of sides
Undecagon (11 sides), because
(n−2) x 180 = 1620
⇒ n−2 = 9
⇒ n=11
500
Find the values of the pronumerals x and y?
180 - 70 - 74 = 36 (Angle Sum of a Triangle)
y = 180 - 78 - 36 = 66 (Straight Angle)
x = 180 - 90 - 66 = 24 (Angle Sum of a Triangle)
Hence, x = 24 and y = 66
500
Give 2 reasons why the following triangle can not exist
2 reasons are:
Angle Sum of this triangle is 181 (NOT 180 degrees)
The largest angle is NOT opposite to the longest side
500
Find the value of x? Show all the workings
(x + 25) + (x + 17) = 3x + 2
2x + 42 = 3x + 2
3x - 2x = 42 - 2
x = 40 (Exterior Angle Theorem)
500
Find the values of x? Show all the workings. Correct to the nearest degree
(4x-10) + (3x+5) + (10x-15) + 90 = 360
17x + 70 = 360
17x = 290
x = 290/17
x = approx 17 degrees