CBSE Class 7 Mathematics Parallel and Intersecting Lines MCQs Set 11

Answer: (c) 4

Explanation:
1. Two intersecting lines cross at exactly one point.
2. Around that point they make 4 angles: two pairs of vertically opposite angles.
3. Eight angles appear only when a transversal cuts two lines at two different points.

Teacher's Note:
1. Draw a quick ✕ and count the gaps between the arms.
2. Do not confuse this with the 8 angles made by a transversal.

Answer: (b) 180°

Explanation:
1. A linear pair is two adjacent angles whose outer arms lie on one straight line.
2. Together they make a straight angle, which is 180°.

Teacher's Note:
1. Linear pair means 'on a line', so think of a straight angle.
2. 90° is the sum for complementary angles, not a linear pair.

Answer: (d) 90°

Explanation:
1. If all four angles at an intersection are equal, each one is 360° ÷ 4 = 90°.
2. Lines that meet at 90° are called perpendicular lines.

Teacher's Note:
1. A right angle is shown by a small square in a figure.
2. 180° is a straight angle, not a meeting angle of two lines.

Answer: (a) a transversal

Explanation:
1. A line crossing two given lines at two different points is a transversal.
2. It makes four angles at each crossing, eight angles in all.

Teacher's Note:
1. 'Trans' means across: the line goes across both lines.
2. A transversal need not be perpendicular to the lines.

Answer: (d) matching arrow marks on the lines

Explanation:
1. Parallel lines are marked with the same arrow mark on each line.
2. A second set of parallel lines in the same figure gets double arrows.
3. The small square at a corner is the mark for perpendicular lines.

Teacher's Note:
1. Arrows for parallel, small square for perpendicular.
2. Look for these marks in every figure before solving.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A is true: vertically opposite angles are always equal.
2. R is true: a linear pair adds up to 180°.
3. Proof of A uses R: ∠a + ∠b = 180° and ∠b + ∠c = 180°, so ∠a = ∠c. Hence R correctly explains A.

Teacher's Note:
1. The linear-pair rule is the reason behind the vertically-opposite rule.
2. Both sums share ∠b, so the other two angles must be equal.

Answer: (d) A is false, but R is true.

Explanation:
1. A is false: parallel lines never meet, however far they are extended.
2. R is true: it is the exact definition of parallel lines.

Teacher's Note:
1. Parallel lines stay the same distance apart everywhere.
2. If a pair of lines meets somewhere, it is not parallel.

Answer: (b) Only Statement II is true.

Explanation:
1. Statement I is false: two straight lines can cross at only one point.
2. Statement II is true: the opposite angles are vertically opposite angles, and these are always equal.
3. So only Statement II is true.

Teacher's Note:
1. If two straight lines shared two points, they would be the same line.
2. Check each statement separately before choosing.

Answer: (c) Both the statements are true.

Explanation:
1. Opposite edges of a square never meet, so they are parallel.
2. Adjacent edges meet at a corner at a right angle, so they are perpendicular.
3. So both statements are true.

Teacher's Note:
1. A square sheet shows both kinds of line pairs.
2. Opposite edges: parallel; adjacent edges: perpendicular.

Answer: (a) 90°

Explanation:
1. A linear pair adds up to 180°.
2. If the two angles are equal, each is 180° ÷ 2 = 90°.
3. So the two lines are perpendicular.

Teacher's Note:
1. Equal parts of a straight angle are right angles.
2. This is how perpendicular lines arise.

Answer: (c) (i)-(q), (ii)-(p), (iii)-(s), (iv)-(r)

Explanation:
1. A linear pair adds up to 180°: (i)-(q).
2. Vertically opposite angles are always equal: (ii)-(p).
3. Perpendicular lines meet at 90°: (iii)-(s).
4. Parallel lines never meet: (iv)-(r). So the answer is (c).

Teacher's Note:
1. Match the easiest pair first, then eliminate options.
2. Only option (c) has both (iii)-(s) and (iv)-(r).

Answer: (d) 130°

Explanation:
1. The angle x and the 50° angle are adjacent angles on the straight line l.
2. So they form a linear pair: x + 50° = 180°.
3. x = 180° − 50° = 130°.

Teacher's Note:
1. Look at which line the two angles share as a straight edge.
2. An obtuse-looking angle like x cannot be 40° or 50°.

Answer: (a) supplementary, that is, they add up to 180°

Explanation:
1. For parallel lines, interior angles on the same side of a transversal add up to 180°.
2. So they are supplementary.
3. They are equal only in the special case when both are 90°.

Teacher's Note:
1. Equal is the rule for alternate and corresponding angles, not for these.
2. Same side interior angles: sum 180°.

Answer: (b) are parallel to each other

Explanation:
1. Equal corresponding angles is the test for parallel lines.
2. So the two lines are parallel to each other.

Teacher's Note:
1. This is the reliable way to check parallel lines, better than judging by eye.
2. One equal pair of corresponding angles is enough.

Answer: (c) the vertically opposite angle of that corresponding angle

Explanation:
1. Step 1: move to the corresponding angle at the other line.
2. Step 2: take the vertically opposite angle of that corresponding angle.
3. This two-step route is also how we prove that alternate angles are equal.

Teacher's Note:
1. Corresponding, then vertically opposite: both steps keep the measure the same.
2. So alternate angles on parallel lines are equal.

Answer: (d) A is false, but R is true.

Explanation:
1. A is false: if the lines are not parallel, the corresponding angles can never be equal.
2. R is true: it states this rule correctly.

Teacher's Note:
1. Equal corresponding angles and parallel lines always go together.
2. So A contradicts R.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Take the common line as a transversal of the two lines.
2. Each line makes 90° with it, so a pair of corresponding angles is 90° and 90°, which are equal.
3. Equal corresponding angles mean the lines are parallel. Both are true and R explains A.

Teacher's Note:
1. This is the idea behind making parallel lines by paper folding.
2. Two right angles in the same position are corresponding angles.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A is true: each of the four angles at one line has a partner in the same position at the other line, giving four pairs.
2. R is true: alternate angles on parallel lines are equal.
3. But R talks about alternate angles and does not explain the counting in A.

Teacher's Note:
1. Both statements are correct facts, but unrelated.
2. Ask: does R tell us why A happens?

Answer: (a) Only Statement II is true.

Explanation:
1. Statement I is false: the eight angles form four pairs of vertically opposite angles, so at most four different measures are possible.
2. Statement II is true: in parallel illusions, truly parallel lines look bent or slanted.
3. So only Statement II is true.

Teacher's Note:
1. Note that the options here list Statement II first.
2. Vertically opposite angles cut the number of possible measures in half.

Answer: (b) 36°

Explanation:
1. Adjacent angles at an intersection form a linear pair.
2. Let the smaller angle be x. Then x + 4x = 180°, so 5x = 180°.
3. x = 36° (the other angle is 144°).

Teacher's Note:
1. Check: 36° + 144° = 180°.
2. Adjacent angles at a crossing always add to 180°.

Answer: (c) 65°

Explanation:
1. Interior angles on the same side of a transversal on parallel lines add up to 180°.
2. Required angle = 180° − 115° = 65°.

Teacher's Note:
1. Same side interior: subtract from 180°.
2. 115° would be the alternate angle, not this one.

Answer: (d) four angles of 72° and four angles of 108°

Explanation:
1. Every one of the eight angles is either equal to 72° or forms a linear pair with a 72° angle.
2. The linear-pair partner is 180° − 72° = 108°.
3. So there are four angles of 72° and four angles of 108°.

Teacher's Note:
1. With parallel lines, one angle fixes all eight.
2. 72° and 108° add to 180°, not 90°.

Answer: (a) (i)-(q), (ii)-(s), (iii)-(p), (iv)-(r)

Explanation:
1. Transversal: a line cutting a pair of lines at two points, so (i)-(q).
2. Point of intersection: the common point of two intersecting lines, so (ii)-(s).
3. Alternate angles: on opposite sides of the transversal, between the lines, so (iii)-(p).
4. Corresponding angles: same position at the two crossings, so (iv)-(r). Answer (a).

Teacher's Note:
1. Options (a) and (c) differ only in (iii) and (iv).
2. 'Same position' always means corresponding.

Answer: (b) 115°

Explanation:
1. The 65° angle (below l) and x (above m) both lie between the parallel lines, on the left of t.
2. So they are interior angles on the same side of the transversal, and they add up to 180°.
3. x = 180° − 65° = 115°.

Teacher's Note:
1. Both angles are inside the parallel lines and on the same side of t.
2. x is obtuse in the figure, which matches 115°.

Answer: (c) 4

Explanation:
1. At each crossing there are only two different measures: an angle and its linear-pair partner.
2. Two crossings can therefore give at most 2 + 2 = 4 different measures.
3. If the lines were parallel, this would drop to just two.

Teacher's Note:
1. Vertically opposite angles at each crossing are equal.
2. Eight different measures is never possible.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. ∠ADC and ∠DAB lie between AB and CD, on the same side of the transversal AD.
2. So they are same-side interior angles, and by R they add up to 180°.
3. Both are true and R is the correct explanation of A.

Teacher's Note:
1. Name the transversal first: here it is AD.
2. Then check that both angles lie between the parallel lines.

Answer: (b) Only Statement II is true.

Explanation:
1. Statement I is false: parallel illusions trick our eyes, so looks alone cannot decide.
2. Statement II is true: the two lines are not in the same plane, and parallel lines must lie in one plane.
3. So only Statement II is true.

Teacher's Note:
1. Parallel lines must be in the same plane and never meet.
2. Measure or reason; do not judge by appearance.

Answer: (d) 102°

Explanation:
1. Same-side interior angles add up to 180°: (2x + 10) + 3x = 180.
2. 5x = 170, so x = 34.
3. The angles are 2 × 34 + 10 = 78° and 3 × 34 = 102°. The larger one is 102° (check: 78 + 102 = 180).

Teacher's Note:
1. 78° is the smaller angle, a common trap.
2. Always put x back to find the actual angles.

Answer: (c) (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q)

Explanation:
1. Corresponding angles are equal: (i) is 125°, so (i)-(r).
2. Same-side interior angle of 125° is 180° − 125° = 55°, so (ii)-(p).
3. Alternate angles are equal: (iii) is 70°, so (iii)-(s).
4. Same-side interior angle of 70° is 180° − 70° = 110°, so (iv)-(q). Answer (c).

Teacher's Note:
1. Equal for corresponding and alternate; subtract from 180° for same-side interior.
2. Work each row on its own.

Answer: (b) 72°

Explanation:
1. Through O draw a line parallel to l (and so also to m).
2. The part of x above this line equals 40° (alternate angle of the 40° at A).
3. The part of x below this line equals 32° (alternate angle of the 32° at B).
4. x = 40° + 32° = 72°.

Teacher's Note:
1. An extra parallel line through the bend splits x into two alternate angles.
2. The bend angle is the sum of the two given angles.