Angles and Their Measure Advanced Geometry

Angles An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.

Name the angles in the figure Naming Angles Name the angles in the figure

Question When an angle is named using three letters, how can you identify the vertex of the angle?

Question Without seeing a figure, is it possible to give another name for ∠MKG? If so, what is it? If not, why not?

Example Name ∠2 in as many different ways as possible.

Measuring Angles Degrees (°) are a common measurement unit for circular arcs. There are 360° in a circle! The measure of an angle is written m∠A or m∠PQR.

Classifying Angles

Example In a coordinate plane, plot the points and sketch angle ABC. Classify the angle. A(5,-1), B(3,-2), C(4,-4) A(-3,1), (-2,2), (-1,4)

Congruent Angles Angles that have the same measure are called congruent angles.

Use a protractor to draw an angle with the given measure. Draw an angle with a measure of 53°.

Use a protractor to draw an angle with the given measure. Draw an angle with a measure of 138°.

Measuring Given Angles. Measure the two angles on the sheet given to you.

Two angles are adjacent angles if they share a common vertex and side, but have no common interior points

Angle Addition Postulate If B is in the interior of AOC, then Thus, the measure of the bigger angle is the sum of the measure of the two smaller ones

Angle Addition Postulate

Using Angle Addition Postulate Find the measure of angle DAB 2. Find the measure of angle CAB

A lawn is watered by a sprinkler that has two fixed spray heads that each spray water in a fan shape. The angle that determines each of the fan shapes is 120. The shaded area in the diagram shows where the two fan shapes overlap. Find the measure of angle 2 30 30 1 2 3