Angles in Parallel Lines — Corresponding, Alternate, and Co-Interior

Angles in Parallel Lines — Corresponding, Alternate, and Co-Interior. Practice questions to deepen understanding of angles formed by parallel lines and a transversal — corresponding, alternate, and co-interior angles. Online math practice with full solutions and step-by-step explanations.

Angles in parallel lines practice — corresponding, alternate, and co-interior (same-side) angles. Theorems and converses with diagrams and explanations.

50 questions

Question 1
2.00 pts

📐 :
corresponding angles?

transversal

Explanation:

💡 :

1: corresponding angles? 🔍

corresponding angles ✨
angles find
ratio
because

2: 📊

Question 2
2.00 pts

🎯 :
angle -∠2?

transversal

Explanation:

Explanation: See the definition and relevant formula above.

Question 3
2.00 pts

🔢 :
parallel lines.
∠1 = 65°.
∠5?

angles 1 -5

Explanation:

💡 :

1: 🔍

! 💡
parallel:
corresponding angles equal

2: 📐

Question 4
2.00 pts

📐 :
angle -∠4?

transversal

Explanation:

💡 :

📊

angles 4 -8

∠4 -∠8

: ∠8

Question 5
2.00 pts

✓ :
because " transversal.
∠3 = 110°, ∠7 = 110°.
parallel lines?

angles 3 -7

Explanation:

💡 :

1: 🔍

! 💡
corresponding angles equal
↓
parallel

2: 📐

Question 6
2.00 pts

🔤 :
parallel lines.
∠2 = 3x + 15°.
∠6 = 75°.
x?

transversal

Explanation:

💡 :

1: 🔍

∠2 -∠6

Yes equal!

2: 📐

Question 7
2.00 pts

📋 Counting:
How many pairs of corresponding angles are there
between two lines cut by a transversal?

two lines and transversal

Explanation:

💡 Detailed explanation:

Step 1: list of all pairs 🔍

The corresponding pairs:

1️⃣ ∠1 and ∠5
2️⃣ ∠2 and ∠6
3️⃣ ∠3 and ∠7
4️⃣ ∠4 and ∠8

Step 2: overall diagram 📊

2,14,36,58,7

Step 3: explanation 💭

🔹 At each intersection there are 4 angles
🔹 Each angle has a "matching position" at the other intersection
🔹 Total: 4 corresponding pairs

Answer: 4 pairs

Question 8
2.00 pts

🔢 :
parallel lines.
∠3 = 125°.
∠7?

angles 3 -7

Explanation:

💡 :

📐

∠3 -∠7

∠7 = ∠3

= 125°

: 125°

Question 9
2.00 pts

❓ :
∠1 = 80°, ∠5 = 100°.
parallel lines?

transversal

Explanation:

💡 :

1: 🔍

∠1 -∠5

∠1 = 80°
∠5 = 100°

80° ≠ 100°

2: 💭

Question 10
2.00 pts

🔤 :
parallel lines.
∠4 = 2x°, ∠8 = x + 50°.
x?

transversal

Explanation:

💡 :

📐

∠4 = ∠8 ()

2x = x + 50

2x - x = 50

x = 50

: 50

Question 11
2.00 pts

📐 angle:
parallel lines.
∠1 = 72°.
∠5 angle...

transversal

Explanation:

💡 :

📐

∠5 = ∠1 = 72°

72° < 90°

angle

:

Question 12
2.00 pts

🌟 :
parallel
corresponding angles?

Explanation:

💡 :

🔍

Question 13
2.00 pts

📐 :
alternate interior angles?

transversal

Explanation:

💡 :

1: alternate interior angles? 🔍

! ✨

corresponding angles
equal
↓
parallel
alternate interior angles ✨
angles
( )

transversal<
Question 14
2.00 pts

🎯 :
angle -∠4?

transversal

Explanation:

Explanation: See the definition and relevant formula above.

Question 15
2.00 pts

🔢 :
parallel lines.
∠3 = 110°.
∠5?

angles 3 -5

Explanation:

💡 :

1: 🔍

! 💡
parallel:
alternate interior angles equal

2: 📐

Question 16
2.00 pts

✓ :
because " transversal.
∠3 = 110°, ∠5 = 110°.
parallel lines?

angles 3 -5

Explanation:

💡 :

1: 🔍

! 💡
alternate interior angles equal
↓
parallel

2: 📐

Question 17
2.00 pts

🔤 :
parallel lines.
∠3 = 3x + 15°.
∠5 = 75°.
x?

transversal

Explanation:

💡 :

1: 🔍

∠3 -∠5

Yes equal!

2: 📐

3x + 15 = 75

3x = 75 - 15

3x = 60
Question 18
2.00 pts

📋 :
alternate interior angles
transversal?

transversal

Explanation:

💡 :

1: 🔍

by/according to:

1️⃣ ∠3 -∠5
2️⃣ ∠4 -∠6

2: 2? 💭

🔹 angles
🔹 transversal

∠1,∠2,∠7,∠8 !

: 2

Question 19
2.00 pts

🔢 :
parallel lines.
∠4 = 135°.
∠6?

angles 4 -6

Explanation:

💡 :

📐

∠4 -∠6

∠6 = ∠4

= 135°

: 135°

Question 20
2.00 pts

❓ :
∠3 = 95°, ∠5 = 85°.
parallel lines?

transversal

Explanation:

💡 :

1: 🔍

∠3 -∠5

∠3 = 95°
∠5 = 85°

95° ≠ 85°

2: 💭

Question 21
2.00 pts

🔤 :
parallel lines.
∠3 = 2x + 20°.
∠5 = 3x - 10°.
x?

transversal

Explanation:

💡 :

📐

∠3 = ∠5

2x + 20 = 3x - 10

20 + 10 = 3x - 2x

30 = x

x = 30

: 30

Question 22
2.00 pts

📐 angle:
parallel lines.
∠3 = 105°.
∠5 angle...

transversal

Explanation:

💡 :

📐

∠5 = ∠3 = 105°

105° > 90°

angle

:

Question 23
2.00 pts

🔢 :
parallel lines. ∠4 = 82°.
find ∠6.

transversal

Explanation:

💡 :

📐

∠4 -∠6

∠6 = ∠4

= 82°

: 82°

Question 24
2.00 pts

🌟 :
parallel
alternate interior angles?

Explanation:

💡 :

🔍

Question 25
2.00 pts

📐 :
co-interior angles (same-side interior)?

transversal

Explanation:

💡 :

1: co-interior angles (same-side interior)? 🔍

! ✨

alternate interior angles
equal
↓
parallel
co-interior angles (same-side interior) ✨
angles
( )

Question 26
2.00 pts

🎯 :
angle - -∠4?

transversal

Explanation:

Explanation: See the definition and relevant formula above.

Question 27
2.00 pts

🔢 :
parallel lines.
∠3 = 115°.
∠6?

angles 3 -6

Explanation:

💡 :

1: 🔍

! 💡
parallel:
co-interior angles (same-side interior)
= 180°

2: 📐

Question 28
2.00 pts

✓ :
because " transversal.
∠3 = 125°, ∠6 = 55°.
parallel lines?

transversal

Explanation:

Explanation: See the definition and relevant formula above.

Question 29
2.00 pts

🔤 :
parallel lines.
∠4 = 2x°, ∠5 = x + 60°.
x?

transversal

Explanation:

💡 :

1: 🔍

∠4 -∠5 -

= 180°

2: 📐

2x + (x + 60) = 180

2x + x + 60 = 180

Question 30
2.00 pts

📋 :
co-interior angles (same-side interior)
transversal?

transversal

Explanation:

💡 :

1: 🔍

-:

1️⃣ ∠3 -∠6
2️⃣ ∠4 -∠5

2: 2? 💭

🔹 angles
🔹 transversal

, !

: 2

Question 31
2.00 pts

🔢 :
parallel lines.
∠4 = 142°.
∠5?

angles 4 -5

Explanation:

💡 :

📐

∠4 + ∠5 = 180°

142 + ∠5 = 180

∠5 = 180 - 142

∠5 = 38°

: 38°

Question 32
2.00 pts

❓ :
∠3 = 100°, ∠6 = 70°.
parallel lines?

transversal

Explanation:

💡 :

1: 🔍

∠3 -∠6 -

∠3 + ∠6 = 100 + 70

= 170°

170° ≠ 180°

2: 💭

Question 33
2.00 pts

🔤 :
parallel lines.
∠3 = 3x - 10°.
∠6 = 2x + 30°.
x?

transversal

Explanation:

💡 :

📐

∠3 + ∠6 = 180°

(3x - 10) + (2x + 30) = 180

3x + 2x - 10 + 30 = 180

5x + 20 = 180

5x = 160

x = 32

: 32

Question 34
2.00 pts

📐 angles :
parallel lines.
∠3 = 73°.
∠6 angle ...

transversal

Explanation:

💡 :

1: ∠6 🔍

∠3 + ∠6 = 180°

73 + ∠6 = 180

∠6 = 107°

2: 📐

∠3 + ∠6 = 73 + 107
Question 35
2.00 pts

🔢 :
parallel lines.
∠4 = 95°.
find ∠5 -∠6.

transversal

Explanation:

💡 :

1: ∠5 🔍

∠4 -∠5 -

∠4 + ∠5 = 180

95 + ∠5 = 180

∠5 = 85°

2: ∠6 📐

∠4
Question 36
2.00 pts

🌟 :
co-interior angles (same-side interior)
parallel lines?

Explanation:

💡 :

🔍

! ✨
parallel:
co-interior angles (same-side interior)
= 180°

? 💭

Question 37
2.00 pts

🔍 :
∠1 -∠7 angles...

transversal

Explanation:

💡 :

1: 🔍

∠1 -∠7:

🔹 ∠1 - ,
🔹 ∠7 - ,

!

2: 💭

❌ No (No )
❌ No ( )
❌ No - ( )

!
Question 38
2.00 pts

🔢 :
parallel lines.
∠1 = 65°.
∠5?

angles 1 -5

Explanation:

💡 :

1: 🔍

∠1 -∠5 !

parallel - equal

2: 📐

∠5 = ∠1

=
Question 39
2.00 pts

🔤 :
parallel lines.
∠1 = 2x + 10°.
∠3 = 3x - 20°.
x?

transversal

Explanation:

💡 :

1: angles 🔍

∠1 -∠3 angles !
( , )

2: 📐

angles equal!

2x +
Question 40
2.00 pts

💡 :
parallel lines. ∠2 = 80°.
find ∠8 because ?

transversal

Explanation:

💡 :

1: 🔍

because :

1️⃣ ∠2→∠6 () → ∠6→∠8 ()
2️⃣ ∠2→∠4 () → ∠4→∠8 ()
3️⃣ ∠2 -∠8 - !

2: 📐

∠2 -∠8 -!

∠2 + ∠8 = 180°

80 + ∠8 = 18
Question 41
2.00 pts

🤔 :
angles
(, , -)?

Explanation:

Explanation: See the definition and relevant formula above.

Question 42
2.00 pts

🎯 :
parallel lines. ∠1 = 72°.
find ∠3, ∠5, ∠7.

transversal

Explanation:

💡 :

1: ∠3 🔍

∠1 -∠3

∠3 = ∠1 = 72°

2: ∠5 📐

Question 43
2.00 pts

🔢 :
parallel lines. ∠1 = 58°.
∠2?

transversal

Explanation:

💡 :

1: ∠1 -∠2 🔍

∠1 -∠5

∠5 = ∠1 = 72°
∠1 -∠2 supplementary angles!
( )

2: 📐

∠1 + ∠2 = 180°
Question 44
2.00 pts

📝 :
parallel because " .
angle 65°.
angle ?

Explanation:

Explanation: See the definition and relevant formula above.

Question 45
2.00 pts

🔤 :
parallel lines.
∠3 = (x/2)°.
∠5 = 45°.
x?

transversal

Explanation:

💡 :

📐

∠3 -∠5

∠3 = ∠5

x/2 = 45

x = 45 × 2

x = 90

: 90

Question 46
2.00 pts

❌ :
: "∠1 -∠8 ".
?

transversal

Explanation:

💡 :

1: 🔍

alternate interior angles?

🔹 angles
🔹 transversal

2: ∠1 -∠8 📐

∠1 - ( )
∠8 - ( )

❌ No !

3: 💭

Question 47
2.00 pts

🏗️ :
parallel.
: ∠3 = 118°, ∠5 = 118°.
parallel?

Explanation:

Explanation: See the definition and relevant formula above.

Question 48
2.00 pts

🔥 :
parallel lines.
∠3 = 2x + 30°.
∠6 = 4x - 30°.
∠3?

transversal

Explanation:

💡 :

1: angles 🔍

∠3 -∠6 -

∠3 + ∠6 = 180°

2: 📐

(2x + 30) + (4x - 30) = 180

2x +
Question 49
2.00 pts

📚 :
parallel?

Explanation:

Explanation: See the definition and relevant formula above.

Question 50
2.00 pts

🌟 :

angles parallel?

Explanation:

💡 :

🔍

! ✨
parallel:

🔹 corresponding angles equal
🔹 alternate interior angles equal
🔹 co-inter