intersecting-lines-and-angles-at-a-point MCQs for UPSC Prelims

26 practice questions on intersecting-lines-and-angles-at-a-point from the Parallel and Intersecting Lines section of the UPSC Prelims syllabus. 26 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

8 Easy 13 Medium 5 Hard

Sample questions

Q1
medium

Assertion (A): When two straight lines intersect, each pair of vertically opposite angles is equal. Reason (R): Two vertically opposite angles together form a linear pair.

  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: C - A is true, but R is false

Vertically opposite angles are indeed equal, so A is true. A linear pair is made of two adjacent angles on a straight line, and vertically opposite angles are not adjacent, so R is false. Since R is false it can neither explain A nor stand on its own.

Q2
medium

Three straight lines are drawn so that no two of them are parallel and no single point lies on all three. How many points of intersection are formed?

  1. A $2$
  2. B $3$
  3. C $6$
  4. D $1$
Show answer and explanation

Correct answer: B - $3$

Each pair of lines gives one crossing, and three lines make three pairs, so there are $3$ points. One point would happen only if all three passed through the same point, which is ruled out. Two points would need a parallel pair. Six is the count for four such lines, not three.

Q3
easy

Two straight lines cross each other. One of the four angles formed measures $55^\circ$. What is the measure of the angle vertically opposite to it?

  1. A $125^\circ$
  2. B $145^\circ$
  3. C $35^\circ$
  4. D $55^\circ$
Show answer and explanation

Correct answer: D - $55^\circ$

Vertically opposite angles are always equal, so the opposite angle is also $55^\circ$. The value $125^\circ$ is the adjacent angle, found by subtracting from $180^\circ$, not the opposite one. Subtracting from $90^\circ$ gives $35^\circ$, and $145^\circ$ comes from subtracting from $200^\circ$, which has no meaning here.

Q4
medium

Two straight lines cross so that one of the four angles formed is $90^\circ$. What can be said about the remaining three angles?

  1. A The opposite one is $90^\circ$ and the other two are $45^\circ$ each
  2. B The three of them add up to $90^\circ$
  3. C All three of them measure $90^\circ$
  4. D Nothing at all can be decided about them
Show answer and explanation

Correct answer: C - All three of them measure $90^\circ$

The angle opposite the right angle equals it, and each angle next to it is $180^\circ - 90^\circ = 90^\circ$, so all four are right angles. Halving to $45^\circ$ ignores the linear pair rule. The remaining three add to $270^\circ$, not $90^\circ$, and the two rules fix every angle, so much can be decided.

Q5
medium

Two straight lines cross at a point, and one of the four angles formed is $130^\circ$. What are the other three angles?

  1. A $40^\circ$, $130^\circ$ and $40^\circ$
  2. B $50^\circ$, $50^\circ$ and $50^\circ$
  3. C $130^\circ$, $130^\circ$ and $130^\circ$
  4. D $50^\circ$, $130^\circ$ and $50^\circ$
Show answer and explanation

Correct answer: D - $50^\circ$, $130^\circ$ and $50^\circ$

Each angle next to the given one is $180^\circ - 130^\circ = 50^\circ$, and the angle opposite it equals $130^\circ$. So the other three are $50^\circ$, $130^\circ$ and $50^\circ$. Making all four equal ignores the linear pair rule, and $40^\circ$ comes from subtracting from $170^\circ$.

Q6
medium

Lines $AB$ and $CD$ cross at $O$, so that $\angle AOC$ and $\angle BOD$ are vertically opposite. If $\angle AOC = 3x$ and $\angle BOD = 75^\circ$, find $x$.

  1. A $105$
  2. B $15$
  3. C $25$
  4. D $35$
Show answer and explanation

Correct answer: C - $25$

Vertically opposite angles are equal, so $3x = 75^\circ$ and $x = 25$. Using $3x + 75 = 180$ gives $35$, which wrongly treats the pair as a linear pair. Using $3x + 75 = 120$ gives $15$, and $105$ is simply $180 - 75$ with the $3$ forgotten.

Q7
medium

Two different straight lines lie on the same flat sheet and never meet, however far they are extended. What must be true about them?

  1. A They are parallel
  2. B They are perpendicular
  3. C They are really the same line
  4. D They meet just beyond the edge of the sheet
Show answer and explanation

Correct answer: A - They are parallel

Two lines in one plane that never meet, no matter how far they run, are parallel by definition. Perpendicular lines do meet, at $90^\circ$. Meeting beyond the sheet would still count as meeting, which the question rules out. The same line drawn twice would share every point.

Q8
easy

A ray stands on a straight line at a point on it. The two angles so formed always add up to

  1. A $180^\circ$
  2. B $270^\circ$
  3. C $360^\circ$
  4. D $90^\circ$
Show answer and explanation

Correct answer: A - $180^\circ$

The two angles together cover the straight angle along the line, which measures $180^\circ$. A total of $90^\circ$ belongs to complementary angles, $360^\circ$ to all the angles around a full turn at a point, and $270^\circ$ to three right angles.

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