1.5 Measuring and Constructing Angles

1.5 Measuring and Constructing Angles

by Mary Lett

​Objective and Standards

• ​Students will be able to define, construct, identify, measure, and name angles, vertex, sides, interior of an angle, exterior of an angle, acute angle, obtuse angle, right angle, straight angle, congruent angles, and angle bisector.

• ​Colorado High School Geometry Standards:

  • ​HSG.CO.A.1: Know precise definitions of angle, … based on the undefined notions of point, line, …

  • ​HSG.CO.D.12: Make formals geometric constructions with a variety of tools and methods (compass and straightedge, …). …

​Vocabulary

• ​Angle: a set of points consisting of two different rays that have the same endpoint.

• ​Vertex: the shared end point of the two rays in the angle

• ​Sides: the two rays that form the angle.

​Vocabulary (continued)

• ​Interior of the angle: the region that contains all of the points between the two sides of the angle

• ​Exterior of the angle: the region that contains all of the points outside the angle

Multiple Choice

A point where two or more lines meet, a corner. HINT: You use this to name an angle!

• Parallel lines

• a vertex

• vertical lines

• transversal

Multiple Choice

Name a point in the interior of <PQR.

• P

• Q

• W

• R

Multiple Select

List all the points that lie on <PQW

• P

• Q

• R

• W

Multiple Choice

Angles are measured using a ______.

• compass

• protractor

• ruler

• prospector

Multiple Choice

_{^{What is the measure of the following angle?}} 

• 120 degrees.

• 175 degrees.

• 60 degres.

• 5 degrees.

Multiple Choice

_{What is the measure of the following angle?}  

• 21 degrees.

• 34 degrees.

• 70 degrees.

• 172 degrees. 

Multiple Choice

Classify this angle  $$\angle AOC$$  

• Right

• Straight

• Obtuse

• Acute

Multiple Choice

Classify this angle  $$\angle BOD$$  

• Right

• Straight

• Obtuse

• Acute

Multiple Choice

Classify this angle  $$\angle AOE$$  

• Right

• Straight

• Obtuse

• Acute

Multiple Choice

Classify this angle  $$\angle AOB$$  

• Right

• Straight

• Obtuse

• Acute

Multiple Choice

• 24°

• 58°

• 68°

• 16°

Multiple Choice

• 37°

• 149°

• 42°

• 72°

Multiple Choice

• 46° and 67°

• 130° and 4°

• 32° and 85°

• 37° and 58°

Multiple Choice

Angle JHG measures 161.

• m∠GHK=80.5,

  m∠KHJ=161

• m∠GHK=161,

  m∠KHJ=80.5

• m∠GHK=80.5,

  m∠KHJ=80.5

• m∠GHK=161,

  m∠KHJ=161

Multiple Choice

$$\overrightarrow{BD}$$  bisects  $$\angle ABC$$  ,  $$m\angle ABD=5\left(x-6\right)$$   and  $$m\angle DBC=2x+9$$ . Find  $$m\angle DBC$$ . 

• $$35\degree$$  

• $$27\degree$$  

• $$11\degree$$  

• $$15\degree$$