Chapter 1.4 Notes: Measure and Classify Angles

Goal: You will name, measure, and classify angles.

• An angle consists of two different rays with the same endpoint.

• The rays are the sides of the angle.

• The endpoint is the vertex of the angle.

• Name the angle above: _____, ______, ______• ____________ is the vertex of the angle.

Ex.1: Name the three angles in the diagram.

Ex.2: Name the three angles in the diagram.

M O

N P

• Classifying Angles:• Angles can be classified as acute, right, obtuse, and

straight.

• Acute angles have a measure greater than 0 and less than 90.

• Right angles have a measure of 90. • Obtuse angles have a measure greater than 90 and

less than 180. • Straight angles have a measure of 180.

• Measuring Angles:• A protractor can be used to approximate the measure of an angle.

• An angle is measured in units called degrees (o).

• Postulate 3 Protractor Postulate:Consider and a point A on one side of . The rays of the form can be matched one to one with the real numbers from 0 to 180.

The measure of is equal to the absolute value of the difference between the real numbers for and .

A

O B

OB��������������

OA��������������

AOB

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EXAMPLE 3 Measure and classify angles

Use the diagram to find the measure of the indicated angle. Then classify the angle.

a. KHJ b. GHK c. GHJ d. GHL

SOLUTION

A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.

• Postulate 4 Angle Addition Postulate:If P is in the interior of , then the measure of

is equal to the sum of the measures of and .

If P is in the interior of , then m RST m RSP m PST

RST

PSTRSPRST

RST

Ex.4: Given that , find and .

145om LKN m LKMm MKN

Ex.5: If find and 72 ,om XYZ m XYW.m ZYW

Ex.6: Given that is a straight angle, find and .

KLMm KLN m NLM

Ex.7: Given that is a right angle, find and .

EFG

m EFH m HFG

• Congruent Angles:• Two angles are congruent angles if they have the

same measure.

Angle measures ar equal Angles are congruent

Ex.8: The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If , what is

?

157om DEG m GKL

Ex.9: Use the diagram below.a. Identify all pairs of congruent angles.b. , , and .

Find the other angle measures in the diagram.

121om TSR 84om QRS 130om PQR

• An angle bisector is a ray that divides an angle into two angles that are congruent.

Ex.10: In the diagram below, bisects , and . Find . m XYZ018m XYW

XYZYW��������������