SME
Grade 10 Math · Problem type
Same-side interior angles
Use this for “ℓ ∥ m and m∠4 = 73°. Find m∠6.”
Diagram
Same-side interior angles 4 and 6: ∠4 = 73°, ∠6 = 107°, adding to 180°.
The lines are parallel (arrows): angles 1, 4, 5 and 8 are 73°; 2, 3, 6 and 7 are 107°.
m∠1 = 73°
m∠4 = 73°
m∠6 = 107°
This is an example. Type your own values to start a new problem.
m∠4
°
+
m∠6
°
=
180°
m∠1
m∠1
calculated · °
Formulas
m∠6 = 180 − m∠4
107 = 180 − 73
m∠4 = m∠1
73 = 73
Assumptions
•
Lines ℓ and m are parallel, and the transversal crosses both.
•
Same-side interior angles (3 and 5, 4 and 6) are between the lines on one side of the transversal; they add to 180°.
•
Angles 1 and 4 are vertical angles, so they are congruent.
Step-by-step
WE KNOW
m∠4 = 73°
FIND
m∠6 (m∠6), m∠1 (m∠1)
Step 1 · Find m∠6 (m∠6)
Use m∠6 = 180 − m∠4
Parallel lines: same-side interior angles add to 180°.
m∠6 = 180 − 73
m∠6 = 107°
Step 2 · Find m∠1 (m∠1)
Use m∠4 = m∠1
Vertical angles are congruent.
m∠1 = m∠4
m∠1 = 73°
Check
Put the numbers back in. Both sides should match.
107 = 180 − 73 ✓
73 = 73 ✓
Topic check
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