GCSE Maths · Higher · Chapter 6: Angles · Lesson 2

Angles in polygons

Grades 4–7About 50 minutesNo calculator38 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Two parallel lines are crossed by a line. One angle is $7 2^{\circ}$ . Find the co-interior angle to it.
[1 mark]
Answer
A2
From chapter 1
Estimate $\frac{48.3 \times 5.1}{0.18}$ by rounding each number to 1 s.f.
[1 mark]
Answer
A3
From chapter 4
The sequence $1, 7, 19, 37, \dots$ is quadratic. Find the coefficient of $n^{2}$ in its $n$ th term.
[1 mark]
Answer
A4
Key Stage 3
Work out $- 8 - (- 2)$ .
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

The diagram shows a pentagon. Work out the size of angle $x$ .

Not drawn accurately

Hint Split the pentagon into triangles from one corner: the angles add to

(5 - 2) \times 18 0^{\circ}

B1
The diagram shows a hexagon. Work out the size of angle $y$ .
[2 marks]
Not drawn accurately
Answer

Example 2

Each interior angle of a regular polygon is $16 8^{\circ}$ . How many sides does it have?

Hint Work out one exterior angle first. The exterior angles add to

36 0^{\circ}

B2
Each interior angle of a regular polygon is $17 2^{\circ}$ . How many sides does it have?
[2 marks]
Answer

Grades 5–6

C1
The interior angles of a polygon add up to $306 0^{\circ}$ . How many sides does the polygon have?
[2 marks]
Answer
C2
The diagram shows a pentagon and four of its exterior angles. Work out the size of angle $y$ .
[3 marks]
Not drawn accurately
Answer

C3
$A B C D$ is a trapezium with $A B$ parallel to $D C$ . Work out the size of angle $D$ .
[3 marks]
Not drawn accurately
Answer
C4
Each interior angle of a regular polygon is $13 2^{\circ}$ more than each exterior angle. How many sides does the polygon have?
[3 marks]
Answer
C5
$A B C D$ is a rhombus and $A C$ is a diagonal. Work out the size of angle $B A C$ .
[2 marks]
Answer
C6
A regular hexagon, a square and a third regular polygon fit together round a point with no gaps. How many sides does the third polygon have?
[2 marks]
Answer

Grades 6–7

D1
Ella says, "If you double the number of sides of a polygon, the sum of its interior angles doubles."
Use a pentagon and a decagon to show that Ella is wrong.
[2 marks]

D2
$A B C D E$ is a regular pentagon. $A B P$ is an equilateral triangle.
(a)
Work out the size of each interior angle of the pentagon.
[2 marks]
Answer
(b)
Work out the size of angle $P A E$ .
[1 mark]
Answer
(c)
Work out the size of angle $A E P$ . Give reasons for your working.
[3 marks]
Total for D2: 6 marks
D3
The interior angles of a pentagon are $(2 x + 10)^{\circ}$ , $(x + 65)^{\circ}$ , $(3 x + 5)^{\circ}$ , $(4 x - 10)^{\circ}$ and $(2 x + 50)^{\circ}$ . Work out the largest angle. You must show your working.
[4 marks]
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can find the angle sum of a polygon and a missing angle.
I can find the number of sides of a regular polygon.
I can use the angles of the special quadrilaterals.

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