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Angle Measurement

Measurement of angles with protractors and addition of angles.

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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 \begin{align*}^\circ\end{align*} symbol.

The Angle Addition Postulate states that if \begin{align*}B\end{align*}B is on the interior of \begin{align*}\angle ADC\end{align*}ADC, then \begin{align*}m \angle ADC = m \angle ADB + m \angle BDC\end{align*}mADC=mADB+mBDC. 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 \begin{align*}m \angle QRT\end{align*}mQRT in the diagram below?

Example D

Draw a \begin{align*}135^\circ\end{align*}135 angle.

Vocabulary

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

Warm-Up Activity/Guided Practice:

1. Use a protractor to measure \begin{align*}\angle RST\end{align*}RST below.

2. What is \begin{align*}m \angle LMN\end{align*}mLMN if \begin{align*}m \angle LMO = 85^\circ\end{align*}mLMO=85 and \begin{align*}m \angle NMO = 53^\circ\end{align*}mNMO=53?

3. If \begin{align*}m \angle ABD = 100^\circ\end{align*}mABD=100, find \begin{align*}x\end{align*}x and \begin{align*}m \angle ABC\end{align*}mABC and \begin{align*}m \angle CBD\end{align*}mCBD?

Practice

1. What is \begin{align*}m \angle LMN\end{align*}mLMN if \begin{align*}m \angle LMO = 85^\circ\end{align*}mLMO=85 and \begin{align*}m \angle NMO = 53^\circ\end{align*}mNMO=53?

2. If \begin{align*}m\angle ABD = 100^\circ\end{align*}mABD=100, find \begin{align*}x\end{align*}x.

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

  1. For an angle \begin{align*}\angle ABC, C\end{align*}ABC,C is the vertex.
  2. For an angle \begin{align*}\angle ABC, \overline{AB}\end{align*}ABC,AB¯¯¯¯¯¯¯¯ and \begin{align*}\overline{BC}\end{align*}BC¯¯¯¯¯¯¯¯ are the sides.
  3. The \begin{align*}m\end{align*}m in front of \begin{align*}m \angle ABC\end{align*}mABC 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. \begin{align*}55^\circ\end{align*}55
  2. \begin{align*}92^\circ\end{align*}92
  3. \begin{align*}178^\circ\end{align*}178
  4. \begin{align*}5^\circ\end{align*}5
  5. \begin{align*}120^\circ\end{align*}120
  6. \begin{align*}73^\circ\end{align*}73

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

Solve for \begin{align*}x\end{align*}x.

  1. \begin{align*}m\angle ADC = 56^\circ\end{align*}mADC=56
  2. \begin{align*}m \angle ADC = 130^\circ\end{align*}mADC=130
  3. \begin{align*}m \angle ADC = (16x - 55)^\circ\end{align*}mADC=(16x55)
  4. \begin{align*}m \angle ADC = ( 9x - 80)^\circ\end{align*}mADC=(9x80)

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