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G-CO.11 Warmup M2-035-A03-V01

Prove parallelogram theorems and their converses, including diagonal and rectangle results.

Use supplementary consecutive angles in a parallelogram to find a missing angle measure

Problem

In parallelogram \(ABCD\), angle \(A=110^{\circ}\). Use consecutive angles to find the missing angle measure.

Unworked quadrilateral configuration showing only the supplied evidence. Open full size
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What this problem is really about

Angles at consecutive vertices share a side, so they form the supplementary pair rather than the equal opposite pair. We’ll confirm that adjacency, write their sum as a straight-angle total, isolate the unknown by subtraction, and add the measures back to verify the relationship.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-CO.11
Category
Geometry
Domain
Congruence
Objective
Prove parallelogram theorems and their converses, including diagonal and rectangle results.
Problem type
Use supplementary consecutive angles in a parallelogram to find a missing angle measure