12 multiple-choice questions, progressively harder.
In the numbered diagram, which angle corresponds to ∠1\angle1∠1?
Solution
Correct answer: C
Angle 1 is northwest at the upper crossing. Angle 5 is northwest at the lower crossing.
The same sector at each crossing defines a corresponding pair.
In the numbered diagram, how are ∠4\angle4∠4 and ∠6\angle6∠6 positioned?
Correct answer: A
Both angles lie between the two crossed lines. Angle 4 is left of the transversal and angle 6 is right of it.
Interior angles on opposite sides of the transversal form an alternate interior pair.
Which pair is same-side exterior in the numbered diagram?
Correct answer: D
Angles 2 and 7 lie outside the strip between the lines, both on the right of the transversal.
Angles 2 and 8 are alternate exterior; angles 3 and 6 are same-side interior; angles 1 and 5 are corresponding.
In the numbered diagram, ℓ∥m\ell\parallel mℓ∥m and m∠1=62∘m\angle1=62^\circm∠1=62∘. Find m∠5m\angle5m∠5.
Correct answer: B
Angles 1 and 5 are corresponding angles of the given parallel lines, so their measures are equal.
m∠5=62∘m\angle5=62^\circm∠5=62∘
In the numbered diagram, ℓ∥m\ell\parallel mℓ∥m and m∠3=48∘m\angle3=48^\circm∠3=48∘. Find m∠5m\angle5m∠5.
Angles 3 and 5 are alternate interior angles. Parallel lines make them congruent.
m∠5=48∘m\angle5=48^\circm∠5=48∘
In the numbered diagram, ℓ∥m\ell\parallel mℓ∥m and m∠6=117∘m\angle6=117^\circm∠6=117∘. Find m∠3m\angle3m∠3.
Angles 3 and 6 are same-side interior angles, so their measures sum to 180 degrees.
m∠3=180∘−117∘=63∘m\angle3=180^\circ-117^\circ=63^\circm∠3=180∘−117∘=63∘
In the numbered diagram, ℓ∥m\ell\parallel mℓ∥m and m∠2=38∘m\angle2=38^\circm∠2=38∘. Find m∠8m\angle8m∠8.
Angles 2 and 8 are alternate exterior angles of parallel lines, so they are congruent.
m∠8=38∘m\angle8=38^\circm∠8=38∘
In the numbered diagram, ℓ∥m\ell\parallel mℓ∥m and m∠4=129∘m\angle4=129^\circm∠4=129∘. Find m∠8m\angle8m∠8.
Angles 4 and 8 occupy corresponding southwest sectors. The lines are given parallel, so the corresponding-angle result applies.
m∠8=129∘m\angle8=129^\circm∠8=129∘
In the numbered diagram, ℓ∥m\ell\parallel mℓ∥m and m∠1=83∘m\angle1=83^\circm∠1=83∘. Find m∠8m\angle8m∠8.
Angles 1 and 8 are same-side exterior angles. For parallel lines their measures are supplementary.
m∠8=180∘−83∘=97∘m\angle8=180^\circ-83^\circ=97^\circm∠8=180∘−83∘=97∘
Parallelism is not given in the numbered diagram. Which pair is nevertheless guaranteed to be congruent?
Angles 1 and 3 are vertical angles formed by two distinct intersecting lines at the upper crossing. The vertical-angle theorem applies there.
Each other option connects different crossings and needs an additional condition.
A transversal crosses two distinct coplanar lines at distinct points. The same-side interior angles on one side measure 72∘72^\circ72∘ and 85∘85^\circ85∘. What does the angle form of Euclid's postulate guarantee?
Add the same-side interior measures.
72∘+85∘=157∘72^\circ+85^\circ=157^\circ72∘+85∘=157∘
The total is below 180 degrees, so the accepted angle postulate guarantees a meeting on that side.
Point PPP lies outside line ℓ\ellℓ in the same plane. How many lines through PPP are parallel to ℓ\ellℓ in Euclidean geometry?
The accepted parallel-through-a-point foundation includes existence and uniqueness.
Existence gives a parallel through PPP; uniqueness says there cannot be a second distinct one.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.