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Geometry. 1.4 Angles and Their Measure. 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. Naming Angles. Name the angles in the figure.

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Geometry

Geometry

1.4 Angles and Their Measure


Angles
Angles

An angleconsists 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.


Naming angles
Naming Angles

  • Name the angles in the figure


Geometry
The measure of an angle can be approximated with a protractor, using units called degrees.Let’s try measuring some….


Congruent angles
Congruent Angles protractor, using units called degrees.

Angles that have the same measure are called congruent angles.


Interior vs exterior
Interior vs Exterior protractor, using units called degrees.

A point is in the interior of an angle if it is between points that lie on each side of the angle

A point is in the exterior of an angle if it is not on the angle or in its interior.


Name the interior and exterior p oints
Name the Interior and Exterior protractor, using units called degrees.Points


Angle addition postulate
Angle Addition Postulate protractor, using units called degrees.

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


Geometry

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


Classifying angles
Classifying Angles 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


Plot the following points
Plot the following Points 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

  • L(-5, 3)

  • M(-1, -1)

  • N(3, 3)

  • Q(5, -1)

  • P(3, -5)


Measure and classify the following angles as acute right obtuse or straight
Measure and classify the following angles as acute, right, obtuse, or straight

  • Angle LMN

  • Angle LMP

  • Angle NMQ

  • Angle LMQ


Geometry
Two angles are obtuse, or straightadjacent angles if they share a common vertex and side, but have no common interior points