Problem preview
G-CO.10 Warmup M2-034-A01-V01

Prove triangle theorems including angle sum, isosceles base angles, midsegment theorem, and medians concurrence.

Find a missing interior angle in a triangle using the 180° angle sum

Problem

In a triangle, \(\text{two}~\text{angles}\) measure \(45^{\circ}\) and \(65^{\circ}\). Find the third angle.

Big Picture

What this problem is really about

The missing interior angle is the remainder after the two known angles account for part of a triangle’s fixed total. We’ll write all three angles in one sum, combine only the known measures, and verify the recovered angle by rebuilding the full total.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-CO.10
Category
Geometry
Domain
Congruence
Objective
Prove triangle theorems including angle sum, isosceles base angles, midsegment theorem, and medians concurrence.
Problem type
Find a missing interior angle in a triangle using the 180° angle sum