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Angle Measurement

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Practice Angle Measurement
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Angle Measurement

Lesson 1.5: Angle Measurement

We measure a line segment’s length with a ruler. Angles are measured with something called a protractor . A protractor is a measuring device that measures how “open” an angle is. Angles are measured in degrees, and labeled with a $^\circ$ symbol.

The Angle Addition Postulate states that if $B$ is on the interior of $\angle ADC$ , then $m \angle ADC = m \angle ADB + m \angle BDC$ . See the picture below.

Ticket In/Ticket Out Activity:

Example A

Measure the three angles using a protractor.

Example B

What is the measure of the angle shown below?

Example C

What is $m \angle QRT$ in the diagram below?

Example D

Draw a $135^\circ$ angle.

Vocabulary

A protractor is a measuring device that measures how “open” an angle is. Angles are measured in degrees , and labeled with a $^\circ$ symbol. A compass is a tool used to draw circles and arcs.

Warm-Up Activity/Guided Practice:

1. Use a protractor to measure $\angle RST$ below.

2. What is $m \angle LMN$ if $m \angle LMO = 85^\circ$ and $m \angle NMO = 53^\circ$ ?

3. If $m \angle ABD = 100^\circ$ , find $x$ and $m \angle ABC$ and $m \angle CBD$ ?

Practice

1. What is $m \angle LMN$ if $m \angle LMO = 85^\circ$ and $m \angle NMO = 53^\circ$ ?

2. If $m\angle ABD = 100^\circ$ , find $x$ .

For questions 3-6, determine if the statement is true or false.

1. For an angle $\angle ABC, C$ is the vertex.
2. For an angle $\angle ABC, \overline{AB}$ and $\overline{BC}$ are the sides.
3. The $m$ in front of $m \angle ABC$ means measure.
4. The Angle Addition Postulate says that an angle is equal to the sum of the smaller angles around it.

For 7-12, draw the angle with the given degree, using a protractor and a ruler.

1. $55^\circ$
2. $92^\circ$
3. $178^\circ$
4. $5^\circ$
5. $120^\circ$
6. $73^\circ$

For 13-16, use a protractor to determine the measure of each angle.

Solve for $x$ .

1. $m\angle ADC = 56^\circ$
2. $m \angle ADC = 130^\circ$
3. $m \angle ADC = (16x - 55)^\circ$
4. $m \angle ADC = ( 9x - 80)^\circ$