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Understanding Right Angles and Triangle Problems: Sample Questions and Solutions

This resource provides sample questions and solutions related to right angles and triangles, including isosceles and equilateral triangles. It covers various angle calculations, applying the Pythagorean theorem to determine whether a triangle is right-angled, and finding angles in different triangle types. Each question illustrates important concepts in geometry, helping students grasp the essentials through worked examples. Ideal for learners looking to enhance their understanding of basic triangle properties and angles.

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Understanding Right Angles and Triangle Problems: Sample Questions and Solutions

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  1. Geometry 90° c a Right Angle Triangle Sample Questions & Solutions b

  2. Question • Find the value of the angle A 100° A 50°

  3. Answer 180 – (100 + 50) 180 - 150 = 30° 100° A 50°

  4. Question • Find the value of the angle E 60° E 80°

  5. Answer 180 – (60 + 80) = 40 so 180 – 40 = 140° 60° E 80°

  6. Question • Find the value of the angles C + D if the 2 sides of the triangle are of equal length (isosceles) 50° D C

  7. Answer 180 – 50 = 130 so 130 ÷ 2 (equal angles) = 65° 50° D C

  8. Question • Find the size of the angles E,F and G if all sides of the triangle are equal in length G F E

  9. Answer E = 60° F = 60° G = 60° as all angles in an equilateral triangle are = 60° G E F

  10. Question • In each of the following triangles, investigate whether or not the triangle is right-angled 14

  11. Answer (a) 16² + 30² = 34² (Pythagoras Theorem a² + b² = c²) so 256 + 900 = 1,156 so 1,156 = 1,156 i.e. Yes, a 90° triangle (b) 12² + 14² = 18² so 144 + 196 = 324 so 340 = 324 i.e. No, not a 90° triangle (c) 80² + 18² = 82² so 6,400 + 324 = 6,724 so 6,724 = 6,724 i.e. Yes, a 90° triangle

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