Math 9 · Unit 5: Angles · Cambridge Lower Secondary Maths Stage 9

Questions

1. 1. How can you inscribe a square in a circle with ruler and compasses?

   • Draw a diameter and bisect it, then join the two halves
   • Draw a diameter, construct its perpendicular bisector to make a second diameter, then join the four ends
   • Draw a chord the same length as the radius six times
   • Draw four 6 cm lines from the centre at 90°, measured with a protractor
   Check

2. 2. A square is inscribed in a circle of radius 6 cm. Its sides should be 8.5 cm. Why?

   • Its perimeter is the circumference, 37.7 cm, and 37.7 ÷ 4 ≈ 8.5
   • Its diagonal is a diameter, 12 cm, and a square with a 12 cm diagonal has sides of √72 ≈ 8.5 cm
   • Each side is 6 cm + 2.5 cm
   • Each side is the radius × 1.5
   Check

3. 3. How do you construct an equilateral triangle with sides of 10 cm?

   • Draw a circle with radius 10 cm and join any three points.
   • Draw a 10 cm line, then draw 10 cm arcs from each end. Join the ends to where the arcs cross.
   • Draw three lines of any length that meet.
   • Draw a 10 cm line and measure 60° with a protractor at one end only.
   Check

4. 4. How can you construct a 60° angle without a protractor?

   • Construct an equilateral triangle and use one of its angles.
   • Bisect a right angle.
   • Draw a straight line and halve it.
   • Construct a square.
   Check

5. 5. Triangle ABC has AB = 9 cm, angle A = 30° and angle B = 60°. What is angle C?

   • 90°
   • 120°
   • 30°
   • 60°
   Check

6. 6. Triangle ABC has AB = 9 cm, angle A = 30° and angle B = 60°. How long should BC be?

   • 3 cm
   • 9 cm
   • 7.8 cm
   • 4.5 cm
   Check

7. 7. In triangle DEF, DE = 8 cm, angle E is a right angle, and the angle outside the triangle at D, on the line ED extended, is 150°. What is angle EDF?

   • 150°
   • 30°
   • 210°
   • 60°
   Check

8. 8. A regular hexagon is inscribed in a circle of radius 7 cm. How long is each side?

   • 7 cm
   • 14 cm
   • 3.5 cm
   • 6 cm
   Check

9. 9. A rectangle is 5 cm tall, and its diagonal makes an angle of 30° with the bottom side. How long should the diagonal measure?

   • 15 cm
   • 8.7 cm
   • 10 cm
   • 5 cm
   Check