Lesson 1-4

Angle Measure

Lesson Outline

Five-Minute Check

Then & Now and Objectives

Vocabulary

Key Concept

Examples

Lesson Checkpoints

Summary and Homework

Then and Now

You measure line segments (Lesson 1–2)

• Measure and classify angles

• Identify and use congruent angles an the bisector of an angle

Objectives

• Measure and classify angles• Obtuse – m > 90• Right – m = 90 (the corner of a piece of paper)• Acute – m < 90

• Identify and use congruent angles an the bisector of an angle

Vocabulary• Degree – one three hundred and sixtieth of a circle• Ray – part of a line with one end point• Opposite rays – are collinear rays with the same end

point (& form a 180 degree angle)

Angle is formed by 2 noncollinear rays with a common endpoint (vertex)

• Sides – composed of rays• Vertex – is the common endpoint• Interior – area between the two rays that form the

angle• Exterior – area not between the two rays that form

the angle

Vocabulary (cont)

Special types of angles:– Right angle – measure equals 90 degrees

– Acute angle – measure is less than 90 degrees

– Obtuse angle – measure is greater than 90 degrees (but less than 180)

• Angle Bisector – a ray that divides an angle into two congruent angles

Example 1

Name all angles that have B as a vertex.

Answer: 5, 6, 7, and ABG

Name the sides of 5.

Answer: and or are the sides of 5.

Write another name for 6.

Answer: EBD, FBD, DBF, and DBE are other names for 6.

Key Concept

• An easy measuring device is the corner of a piece of notebook paper (or computer paper). It is a right angle.

Example 2a

Measure TYV and classify it as right, acute, or obtuse.

TYV is marked with a right angle symbol, so measuring is not necessary.

Answer: is a right angle.

Example 2b

Measure WYT and classify it as right, acute, or obtuse.

Use a protractor to find that .

Answer: >is an obtuse angle.

Example 2c

Measure TYU and classify it as right, acute, or obtuse.

Use a protractor to find that m TYU = 45° .

Answer: Since 45 < 90, then TYU is an acute angle.

Example 3INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH HCI, mGBH = 2x + 5, and mHCI = 3x – 10.

GBH HCI Given

Step 1 Solve for x.

Example 3 cont

mGBH = mHCI Definition of congruent angles

2x + 5 = 3x – 10 Substitution

2x + 15 = 3x Add 10 to each side.

15 = x Subtract 2x from each side.

Step 2 Use the value of x to find the measure of either angle.

Answer: mGBH = 35, mHCI = 35

mGBH = 2x + 5 Given

= 2(15) + 5 Substitution, x = 15

= 30 + 5 = 35 Simplify.

Lesson Checkpoints

Summary & Homework

• Summary:– Angles are named by 3 points with the vertex in

the middle (or by vertex letter if no confusion)– Angles are classified as acute, right, or obtuse

according to their measure– An angle bisector is a ray that divides an angle

into two congruent angles (halves)• Ray is equidistance from the sides of the angle

• Homework: – pg 41-3: 30-35, 39-42