Class 9 Linear Pair and Vertically Opposite Angles — 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. The two angles of a linear pair add up to how many degrees?
A90 deg
B180 deg
C270 deg
D360 deg
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Answer: B) 180 deg
By the Linear Pair Axiom, if a ray stands on a line the two adjacent angles formed are supplementary, so they sum to 180 deg.
2. If one of the four angles at the intersection of two lines is 100 deg, what is the sum of the remaining three angles?
A235
B285
C520
D260
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Answer: D) 260
Total around a point = 360 deg, so remaining = 360 - 100 = 260 deg.
3. Three rays OA, OB, OC are drawn on one side of line PQ from point O on it, with no overlaps. If angle POA = 50 deg, angle AOB = 60 deg, angle BOC = 40 deg, find angle COQ.
A60
B27
C30
D33
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Answer: C) 30
All angles on one side of line PQ at O sum to 180 deg. So angle COQ = 180 - (50 + 60 + 40) = 180 - 150 = 30 deg.
4. Two lines cut each other at O. One angle is 4 times its adjacent angle. Find the measure of the smaller angle of this linear pair.
A40
B72
C32
D36
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Answer: D) 36
Let small = a, large = 4a, linear pair: a + 4a = 180, 5a = 180, a = 36 deg.
5. Two lines AB and CD intersect at O. Ray OE is the bisector of angle BOD. If angle AOC = 70 deg, find angle COE (where E lies in the region of angle BOD).
A130
B145
C160
D290
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Answer: B) 145
Angle BOD is vertically opposite angle AOC, so angle BOD = 70 deg. OE bisects it, so angle BOE = 35 deg. Angle COB is a linear pair with angle AOC, so angle COB = 180 - 70 = 110 deg. Then angle COE = angle COB + angle BOE = 110 + 35 = 145 deg.