# Solve for Unknown Angles — Angles and Lines at a Point

### New York State Common Core Math Geometry, Module 1, Lesson 6

Worksheets for Geometry, Module 1, Lesson 6

Student Outcomes

• Students review formerly learned geometry facts and practice citing the geometric justifications in anticipation of unknown angle proofs.

Solve for Unknown Angles — Angles and Lines at a Point

Classwork

Opening Exercise

Determine the measure of the missing angle in each diagram.

What facts about angles did you use?

Discussion

Two angles ∠𝐴𝑂𝐶 and ∠𝐶𝑂𝐵, with a common side 𝑂𝐶, are _________ if 𝐶 belongs to the interior of ∠𝐴𝑂𝐵. The sum of angles on a straight line is 180°, and two such angles are called a linear pair. Two angles are called supplementary if the sum of their measures is _______; two angles are called complementary if the sum of their measures is ______. Describing angles as supplementary or complementary refers only to the measures of their angles. The positions of the angles or whether the pair of angles is adjacent to each other is not part of the definition.

In the figure, line segment 𝐴𝐷 is drawn.
Find 𝑚∠𝐷𝐶𝐸.

The total measure of adjacent angles around a point is _______.
Find the measure of ∠𝐻𝐾𝐼.

Vertical angles have measure. Two angles are vertical if their sides form opposite rays.
Find 𝑚∠𝑇𝑅𝑉.

Example
Find the measures of each labeled angle. Give a reason for your solution.

Exercises
In the figures below, 𝐴𝐵, 𝐶𝐷, and 𝐸𝐹 are straight line segments. Find the measure of each marked angle, or find the unknown numbers labeled by the variables in the diagrams. Give reasons for your calculations. Show all the steps to your solutions.

For Exercises 6–12, find the values of 𝑥 and 𝑦. Show all work.

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