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G-CO.9 Warmup M2-036-A12-V01

Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.

Combine line, angle, and perpendicular-bisector facts in a multi-step problem

Problem

Angle \(A\) measures \(65^{\circ}\), and angle \(B\) is vertical to angle \(A\). What is the measure of angle \(B\)?

Unworked line or perpendicular-bisector configuration showing only supplied evidence. Open full size
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What this problem is really about

At an intersection, the directly opposite region uses equality while an adjacent region uses a supplementary relationship. We’ll locate the requested angle relative to the given one, classify the pair before doing arithmetic, transfer the measure through congruence, and distinguish the unused linear-pair value.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-CO.9
Category
Geometry
Domain
Congruence
Objective
Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.
Problem type
Combine line, angle, and perpendicular-bisector facts in a multi-step problem