Lemmara logoLemmaraWorked solution

4024/21 May/Jun 2020, Question 7: Interior and Exterior Angles of Polygons

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use the octagon's 135° angle and the quadrilateral's angles 3x°, 103° and (x + 20)° to form and solve an equation for x.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Form an equation in x from the quadrilateral's angles and the octagon's interior angle, then solve it.

  1. 1Exterior angle of a regular octagon = 360 ÷ 8 = 45°, so the quadrilateral's angle on AB is 180 − 135 = 45°
  2. 2Angles in a quadrilateral: 3x + 103 + x + 20 + 45 = 360
  3. 34x + 168 = 360
  4. 44x = 192
  5. 5x = 48

Answer48

Part (bi) · 3 marks

Find angle PQT using PS parallel to QR, angle PSQ = 32°, and TQ as a diameter, giving reasons.

  1. 1angle PTQ = angle PSQ = 32° (angles in the same segment)
  2. 2angle TPQ = 90° (angle in a semicircle, TQ is a diameter)
  3. 3angle PQT = 180 − 90 − 32 = 58° (angles in a triangle)

Answer58

Part (bii) · 2 marks

Find angle QRS using the circle geometry and QR = RS.

  1. 1angle SQR = angle PSQ = 32° (alternate angles, PS parallel to QR)
  2. 2angle QSR = 32° (triangle QRS is isosceles, QR = RS)
  3. 3angle QRS = 180 − 32 − 32 = 116°

Answer116

Part (biii) · 1 mark

Find angle TQS.

  1. 1angle PSR = 32 + 32 = 64°, so angle PQR = 180 − 64 = 116° (opposite angles of a cyclic quadrilateral)
  2. 2From earlier parts, angle PQT = 58° and angle SQR = 32°
  3. 3angle TQS = angle PQR − angle PQT − angle SQR
  4. 4angle TQS = 116 − 58 − 32 = 26°

Answer26

Stuck on a step? Read the free lesson: Interior and Exterior Angles of Polygons

Practise more interior and exterior angles of polygons questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on interior and exterior angles of polygons

Also searched as: 4024/21/M/J/20 · 4024_s20_qp_21 · 4024 s20 21 · question 7.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.