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A pair of parallel lines is intersected by a transversal such that ∠1 and ∠2 form a pair of interior angles on the same side of the transversal. If m\angle 1=65°, what is the measure of ∠2?
95°
65°
115°
145°
115°
Interior angles on the same side of a transversal intersecting parallel lines are supplementary. Just subtract the given angle from 180°.
Two parallel lines intersected by a transversal, angle 1 = 65°, angle 1 and angle 2 are interior angles on the same side of the transversal.
∠1+∠2=180°
Interior angles on the same side of a transversal intersecting parallel lines are supplementary. Just subtract the given angle from 180°.
Confusing interior angles on the same side (supplementary) with alternate interior or corresponding angles (equal).
Identify Relationship
When two parallel lines are intersected by a transversal, the pair of interior angles on the same side are supplementary (they sum to 180°).
∠1+∠2=180°
Substitute Known Values
Substitute the given value ∠1=65° into the supplementary angle equation.
65°+∠2=180°
Calculate Measure
Solve for ∠2 by subtracting 65° from 180°.
∠2=180°−65°=115°
C is correct because the sum of interior angles on the same side of a transversal intersecting parallel lines is 180°, so 180° - 65° = 115°.
This concept is foundational for solving geometry problems involving cyclic quadrilaterals and polygon exterior angles, where interior angle sum properties are frequently used.
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