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Grade 8–9 · Geometry
Angles in Triangles and Quadrilaterals: Full Guide
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    A triangle has angles 55°, 65° and x. Find x. (basic)
    (2)
    55° 65° x
  2. 2
    A right-angled triangle has one other angle of 35°. Find the third. (right-angled)
    (2)
    A90°B35°Cx
  3. 3
    Isosceles triangle, apex 80°. Find each base angle. (isosceles)
    (2)
    ? ? 80°
  4. 4
    Isosceles triangle, base angles 65° each. Find the apex. (isosceles)
    (2)
    65° 65° ?
  5. 5
    Interior angles 70° and 50°; find the exterior angle at the third vertex. (exterior)
    (2)
    xA70°B50°C
  6. 6
    Triangle angles are x, x and 4x. Find x. (solve)
    (2)
  7. 7
    Triangle angles are 2x, 3x and 4x. Find the largest angle. (solve)
    (2)
  8. 8
    Quadrilateral angles 120°, 80°, 70° and x. Find x. (quad)
    (2)
  9. 9
    In parallelogram ABCD below, Â = 110°. Determine the size of x, giving a reason.
    (2)
    A110°BxCD
  10. 10
    Two angles of a triangle are equal; the third is 80°. Find each equal angle. (isosceles)
    (2)
    AxBxC80°
TOTAL: 20 marks
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