IGCSEMathsEdexcelMaths AFoundationExam Questions4. Geometry & TrigonometryAngles in Polygons & Parallel Lines

Angles in Polygons & Parallel Lines (Edexcel IGCSE Maths A: Foundation): Exam Questions

Exam code: 4MA1

21 mins5 questions
1
Sme Calculator5 marks
Geometric diagram shows parallel lines AB and DE with intersecting triangle BCF. Angles marked are 39° at B and 63° at F. Angle x is within triangle.

A B C is parallel to D E F G
B C space equals space B F
Angle A B E space equals space 39 degree
Angle space C F G space equals space 63 degree

Work out the size of angle x.
Give a reason for each stage in your working.

How did you do?

2
Sme Calculator5 marks

The diagram shows two congruent regular pentagons drawn inside a regular octagon.

Octagon with two inner pentagons sharing vertex C. Angles A, B marked. Text on right: "Diagram NOT accurately drawn".

One side of each pentagon lies along a side of the octagon.

A B is a side of the octagon.
A C is a side of one of the pentagons.
B C is a side of the other pentagon.

Work out the size of angle y.
Show your working clearly

How did you do?

3
Sme Calculator3 marks

Here is a 9-sided regular polygon A B C D E F G H J, with centre O

Irregular polygon JABCDEFG with an interior triangle DEK and angle x° shown. Text indicates the diagram is not accurately drawn.

O D K and F E Kare straight lines.

Work out the value of x

How did you do?

4
Sme Calculator4 marks

The diagram shows two triangles A B E and E C D

Triangle diagram with angles labeled: angle A is x degrees, angle D is 42 degrees, and angle at point B is 296 degrees. Note: Diagram not accurately drawn.

Triangle A B E is isosceles with A E space equals space E B
A D E and E B C are straight lines.

Angle C D E space equals space 42 degree
The reflex angle E C D space equals space 296 degree
Angle B A E space equals space x degree

Work out the value of x

How did you do?

5a1 mark
Three intersecting lines with angles marked: 125 degrees at point B, 32 degrees at point F, and variable y and x degrees at points C and G. Diagram not to scale.

A B C Dand E F G Hare straight lines.
K F B J spaceand M G C Lare parallel straight lines.

angle space A B J space equals space 125 degree space space space space space space angle space B F G space equals space 32 degree space space space space space space space angle space F G M space equals space x degree space space space space space space space angle space L C D space equals space y degree

Write down the value of x

How did you do?

5b
Sme Calculator3 marks

(i) Work out the value of y

(ii) Give a reason for your answer to (b) (i)

How did you do?