corresponding-and-alternate-angles MCQs for UPSC Prelims

27 practice questions on corresponding-and-alternate-angles from the Parallel and Intersecting Lines section of the UPSC Prelims syllabus. 27 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

8 Easy 14 Medium 5 Hard

Sample questions

Q1
easy

A transversal cuts two parallel lines and one of the eight angles formed is a right angle. What are the other seven angles?

  1. A All seven are $90^\circ$
  2. B They are $90^\circ$ and $180^\circ$ turn by turn
  3. C Four are $90^\circ$ and three are $45^\circ$
  4. D They cannot be found from this information
Show answer and explanation

Correct answer: A - All seven are $90^\circ$

A right angle at one crossing makes all four angles there $90^\circ$, and the corresponding angles at the other crossing repeat them, so every one of the eight is $90^\circ$. Nothing halves an angle to $45^\circ$. An angle of $180^\circ$ is a straight angle, not one of these eight, and the parallel properties settle the answer completely.

Q2
medium

Lines $l$ and $m$ are parallel and a transversal cuts them, meeting the upper line $l$ at $P$ and the lower line $m$ at $Q$. The interior angle at $P$ on the left of the transversal is $125^\circ$. Find the interior angle at $Q$ on the left of the transversal.

  1. A $55^\circ$
  2. B $65^\circ$
  3. C $125^\circ$
  4. D $35^\circ$
Show answer and explanation

Correct answer: A - $55^\circ$

The two angles are interior and on the same side of the transversal, so they are co-interior and add to $180^\circ$, giving $180^\circ - 125^\circ = 55^\circ$. Repeating $125^\circ$ would treat them as alternate interior angles, which lie on opposite sides. Subtracting from $160^\circ$ gives $35^\circ$ and from $190^\circ$ gives $65^\circ$.

Q3
medium

Assertion (A): Alternate interior angles formed when a transversal cuts two parallel lines are equal. Reason (R): A transversal cuts the two lines at two different points.

  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: B - Both A and R are true, but R is not the correct explanation of A

A is a true property of parallel lines cut by a transversal. R is also true, since a transversal by definition meets the lines at two distinct points. But meeting at two points happens for non-parallel lines as well, where the alternate interior angles are unequal, so R does not explain A.

Q4
medium

Assertion (A): Co-interior angles formed when a transversal cuts two parallel lines add up to $180^\circ$. Reason (R): Co-interior angles are always equal to each other.

  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

A is the correct co-interior property for parallel lines. R is false: co-interior angles are supplementary, and they are equal only in the single case where both are $90^\circ$. So A stands while R does not.

Q5
easy

Which property lets us say that two interior angles on opposite sides of a transversal cutting two parallel lines are equal?

  1. A Co-interior angles add up to $180^\circ$
  2. B A linear pair adds up to $180^\circ$
  3. C Alternate interior angles are equal
  4. D Vertically opposite angles are equal
Show answer and explanation

Correct answer: C - Alternate interior angles are equal

Interior angles on opposite sides of the transversal are exactly the alternate interior pair, and for parallel lines they are equal. The co-interior rule is about interior angles on the same side. Vertically opposite angles and linear pairs live at a single crossing point, so neither links the two crossings.

Q6
medium

Assertion (A): Corresponding angles are equal whenever a transversal cuts any two lines. Reason (R): Corresponding angles are the angles that lie in matching positions at the two crossing points.

  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: D - A is false, but R is true

Corresponding angles come out equal only when the two lines are parallel, so A is false as stated for any two lines. R correctly describes where corresponding angles sit, so R is true. A false assertion with a true reason is the last choice.

Q7
hard

A transversal cuts two parallel lines. A pair of alternate interior angles measures $(5x - 20)^\circ$ and $(3x + 10)^\circ$. What is the measure of the interior angle that forms a co-interior pair with the first of these two angles?

  1. A $125^\circ$
  2. B $15^\circ$
  3. C $35^\circ$
  4. D $55^\circ$
Show answer and explanation

Correct answer: A - $125^\circ$

Equal alternate interior angles give $5x - 20 = 3x + 10$, so $x = 15$ and each angle is $55^\circ$. A co-interior partner adds with it to $180^\circ$, so it measures $180^\circ - 55^\circ = 125^\circ$. Choosing $55^\circ$ stops one step early, $15^\circ$ is the value of $x$, and $35^\circ$ is the complement rather than the supplement.

Q8
hard

A transversal cuts parallel lines $l$ and $m$, meeting the upper line $l$ at $P$ and the lower line $m$ at $Q$. At $P$ the angle above $l$ and left of the transversal is $(3x)^\circ$, and at $Q$ the angle above $m$ and left of the transversal is $(x + 50)^\circ$. Find the angle at $Q$ that lies above $m$ and right of the transversal.

  1. A $75^\circ$
  2. B $95^\circ$
  3. C $105^\circ$
  4. D $25^\circ$
Show answer and explanation

Correct answer: C - $105^\circ$

The two given angles are corresponding, so $3x = x + 50$, giving $x = 25$ and each angle $75^\circ$. At $Q$, the angle above $m$ on the right forms a linear pair with the $75^\circ$ angle, so it is $180^\circ - 75^\circ = 105^\circ$. Stopping at $75^\circ$ answers the wrong angle, $25^\circ$ is the value of $x$, and $95^\circ$ comes from subtracting from $170^\circ$.

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