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Angle Calculation Excercise: Solve Missing Angles and Circle Properties

Practice finding missing angles in triangles, circles, and semicircles. Calculate the diameter, circumference, and area of a circle. Simplify trigonometry problems step by step.

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Angle Calculation Excercise: Solve Missing Angles and Circle Properties

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  1. Reminder - don’t copy a = (180 – 40)  2 = 70° b = a = 70° e° c° 40° c = 180 – 40 = 140° a° d° b° d = (180 – 140)  2 = 20° e = d = 20° NB: b + d = 70 + 20 = 90° So the large triangle is right-angled.

  2. Triangles Inside Semi-Circles Rule: any triangle drawn inside a semi-circle is right-angled. ie a° b° a = 90 b = 90

  3. Exs Find the missing angles ! a 35° 25° x° e d c b y° x = 90 a = 90 – 25 = 65 b = 25 y = 180 - 90 - 35 c = 180 – 25 - 25 = 130 = 55 d = 180 – 130 = 50 e = a = 65

  4. Ex Find (i) diameter (ii) circumference (i) d2 = 102 + 242 = 100 + 576 = 676 d d = 676 = 26 10cm 24cm Diameter = 26cm (ii) C = d = 3.14 X 26 = 81.64 = 81.6cm

  5. Ex Find (i) x (ii) area of triangle. (i) r = 8.5 so d = 17 x 8cm 8.5cm x 8 17 x2 = 172 - 82 = 289 - 64 = 225 x = 225 = 15cm (ii) Area = base X height  2 = 8 X 15  2 = 60cm2

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