Class 7 Exterior Angle Property — practice questions with answers
Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. The exterior angle of a triangle is equal to the sum of its two ______ interior angles.
Ainterior opposite
Badjacent
Cright
Dexterior
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Answer: A) interior opposite
By the exterior angle property, an exterior angle equals the sum of the two interior opposite (remote) angles.
2. An exterior angle of a triangle is 85 deg. The two interior opposite angles can be:
A40 deg and 45 deg
B45 deg and 50 deg
C30 deg and 60 deg
D85 deg and 85 deg
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Answer: A) 40 deg and 45 deg
The two interior opposite angles must add up to 85 deg. Only 40 + 45 = 85.
3. The exterior angle property says the exterior angle equals the sum of interior opposite angles because the exterior and adjacent interior angle form 180 deg and all three interior angles also sum to:
A180 deg
B90 deg
C270 deg
D360 deg
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Answer: A) 180 deg
Angle sum property: the three interior angles of a triangle sum to 180 deg; combining with the linear pair gives the exterior angle property.
4. The exterior angle of an isosceles triangle, formed by extending the base, is 130 deg. The two base angles are equal. Find each base angle.
A100
B55
C50
D45
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Answer: C) 50
Extending the base at one base vertex: the exterior angle and the base angle form a linear pair, so base angle = 180 - 130 = 50 deg. Check: the two base angles are equal (50 each), apex = 180 - 2(50) = 80, and exterior at base vertex = apex + other base = 80 + 50 = 130. Consistent. Each base angle = 50 deg.
5. In triangle ABC, side BC is produced both ways. The exterior angle on one side at C is 112 deg and the exterior angle at B (other side) is 121 deg. Using exterior angle and angle-sum reasoning, find the interior angle A.
A48
B58
C106
D53
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Answer: D) 53
Interior B = 180 - 121 = 59; interior C = 180 - 112 = 68. Interior A = 180 - 59 - 68 = 53 deg.