SME
Grade 10 Math · Problem type
Alternate interior angles
Use this for “ℓ ∥ m and m∠1 = 118°. Find m∠3 and m∠6.”
Diagram
Alternate interior angles 3 and 6: ∠3 = 62°, ∠6 = 62°, equal.
The lines are parallel (arrows): angles 1, 4, 5 and 8 are 118°; 2, 3, 6 and 7 are 62°.
m∠1 = 118°
m∠3 = 62°
m∠6 = 62°
This is an example. Type your own values to start a new problem.
m∠3
°
=
180°
−
m∠1
°
m∠6
m∠6
calculated · °
Formulas
m∠3 = 180 − m∠1
62 = 180 − 118
m∠6 = m∠3
62 = 62
Assumptions
•
Lines ℓ and m are parallel, and the transversal crosses both.
•
Angles 1 and 3 make a straight line, so they add to 180°.
•
Alternate interior angles (3 and 6, 4 and 5) are between the lines on opposite sides of the transversal; they are congruent.
Step-by-step
WE KNOW
m∠1 = 118°
FIND
m∠3 (m∠3), m∠6 (m∠6)
Step 1 · Find m∠3 (m∠3)
Use m∠3 = 180 − m∠1
A linear pair adds to 180°.
m∠3 = 180 − 118
m∠3 = 62°
Step 2 · Find m∠6 (m∠6)
Use m∠6 = m∠3
Parallel lines: alternate interior angles are congruent.
m∠6 = 62°
Check
Put the numbers back in. Both sides should match.
62 = 180 − 118 ✓
62 = 62 ✓
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Parallel and perpendicular lines: transversals and proofs
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Same-side interior angles
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