Class 9 Exterior Angle of a Triangle — practice questions with answers
Geometry — Lines and Angles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. An exterior angle of a triangle is equal to:
Athe interior angle next to it
Bthe sum of the two interior opposite angles
C180° minus the sum of the interior opposite angles
Dhalf the sum of all three angles
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Answer: B) the sum of the two interior opposite angles
Exterior angle theorem: if a side of a triangle is produced, the exterior angle formed equals the sum of the two interior opposite angles.
2. The interior angles of a triangle are 40°, 60° and 80°. Which is its largest exterior angle?
A100°
B140°
C160°
D120°
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Answer: B) 140°
Exterior angles are 180° − 40° = 140°, 180° − 60° = 120° and 180° − 80° = 100°. The largest sits next to the smallest interior angle: 140°.
3. A wall shelf rests on a slanting brace, forming a right triangle with the wall. The brace meets the shelf at 35°. What angle does the brace make with the wall?
A55°
B35°
C145°
D125°
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Answer: A) 55°
Wall ⟂ shelf, so the triangle has angles 90°, 35° and the angle at the wall. The exterior angle at the brace–shelf corner is 180° − 35° = 145° = 90° + (angle at wall), giving 55°.
4. In the figure, the exterior angle at C is 2x and the interior opposite angles are (x + 15)° and 45°. Find x.
A45
B30
C75
D60
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Answer: D) 60
2x = x + 15 + 45, so x = 60. Check: exterior angle 120° = 75° + 45°.
5. In △ABC, ∠A = 64°. The bisector of ∠ABC and the bisector of the exterior angle ∠ACD meet at E. Find ∠BEC.