Class 9 Parallel Lines and a Transversal — 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. A line that intersects two or more lines at distinct points is called a ______.
Atransversal
Bbisector
Cperpendicular
Dmedian
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Answer: A) transversal
By definition, a line cutting two or more lines at distinct points is a transversal.
2. Lines l and m are parallel, cut by transversal t. Corresponding angles are 3x and 75 deg. Find x.
A27
B50
C25
D23
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Answer: C) 25
Corresponding angles are equal: 3x = 75, so x = 25.
3. A transversal cuts two parallel lines. An interior angle and its co-interior partner are in the ratio 4 : 5. Find the smaller angle (deg).
A80
B72
C160
D88
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Answer: A) 80
Co-interior angles sum to 180. Ratio 4:5 means 4k + 5k = 180, 9k = 180, k = 20. Smaller = 4 x 20 = 80 deg.
4. In a railway diagram, two parallel rails are crossed by a sleeper (cross beam) acting as a transversal. The acute angle and obtuse angle the sleeper makes with a rail are in the ratio 2 : 7. Find the obtuse angle (deg).
A280
B140
C125
D155
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Answer: B) 140
Acute + obtuse = 180 (linear pair). Ratio 2:7 gives 2k + 7k = 180, 9k = 180, k = 20. Obtuse = 7 x 20 = 140 deg.
5. AB || CD. A point E lies between them. EF is drawn so that angle BAE = 35 deg (at AB) and angle DCE = 25 deg (at CD), both measured toward E. Drawing a line through E parallel to AB and CD, the reflex/total angle AEC = 35 + 25. Find angle AEC (deg).
A60
B66
C120
D54
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Answer: A) 60
Draw a line through E parallel to AB and CD. By alternate interior angles, the part of angle AEC toward AB = 35 deg and the part toward CD = 25 deg. So angle AEC = 35 + 25 = 60 deg.