Section 04
Exercise 13 — Parallelism
Work through the four question types in order: recall, reasoning, calculation, then multiple choice. Every answer is one click away, so attempt first and reveal after.
1 · Complete each of the following
1If a straight line is perpendicular to one of two parallel straight lines, then it is ___ to the other line in the plane.
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perpendicular
2If two straight lines are parallel to a third straight line, then they are ___.
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parallel
3If two straight lines are perpendicular to a third line in the plane, then these two lines are ___.
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parallel
4When a transversal cuts two parallel lines, each two corresponding angles are ___ in measure.
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equal
5When a transversal cuts two parallel lines, each two interior angles on the same side are ___.
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supplementary (sum 180°)
2 · True or false — and why
Two alternating exterior angles between parallel lines are supplementary.
A transversal meets the two lines it cuts at two different points.
If two corresponding angles are equal, the two lines must be parallel.
Co-interior angles are always equal.
3 · Find the value of x
1Corresponding angles: (3x + 15)° and 75°.
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3x + 15 = 75 ⟹ x = 20
2Co-interior angles: (2x + 10)° and (3x + 20)°.
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2x + 10 + 3x + 20 = 180 ⟹ 5x = 150 ⟹ x = 30
3Alternating interior angles: (4x − 12)° and (2x + 30)°.
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4x − 12 = 2x + 30 ⟹ 2x = 42 ⟹ x = 21
4Angles on a straight line: (3x + 40)° and (2x + 70)°.
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3x + 40 + 2x + 70 = 180 ⟹ 5x = 70 ⟹ x = 14
5MN ∥ ZY, CA ⊥ CE, m(∠MDC) = (2x − 3)°, m(∠ABY) = (3x + 8)°.
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Draw CF ∥ MN ∥ ZY: (2x − 3) + (3x + 8) = 90 + 90 ⟹ 5x = 85 ⟹ x = 17
6Rowing oars: m(∠1) = (2x − 6)°, m(∠2) = (3x − 29)°, x = 23.
Show solution
m(∠1) = 40°, m(∠2) = 40°. Equal corresponding angles ⟹ the oars are parallel.
4 · Multiple choice
1If L₁, L₂ and L₃ are three lines in the same plane with L₃ ∥ L₁ and L₃ ∥ L₂, then:
2If L₂ ⊥ L₁ and L₃ ∥ L₁ in the same plane, then L₂ ___ L₃:
3Two parallel lines are cut by a transversal. One interior angle is 108°. The co-interior angle equals:
4Which pair is NOT necessarily equal between two parallel lines?
5 · Applied problems
Road safety
A pedestrian crossing runs across a straight road. The crossing lines are parallel and the kerb acts as a transversal. If one marked angle is (2x + 30)° and the co-interior angle is (3x + 50)°, then 5x + 80 = 180, so x = 20.
Rowing on the Nile
With m(∠1) = (2x − 6)° and m(∠2) = (3x − 29)° at x = 23, both angles measure 40°. Equal corresponding angles prove the left oars are parallel.