1.1.3 Measuring and Constructing Angles (continued)

In the given figure, ∠ COD is one part of the larger angle ∠ COB , where the second part is ∠ DOB . So, by the Angle Addition Postulate, m ∠ COB = m ∠ COD + m ∠ DOB . Use the Angle Addition Postulate to find m ∠ COD . From the previous example we know that ∠ DOB = 65°. (Remember, ∠ DOB and ∠ BOD are the same angle.) Use the protractor to find m ∠ COB : m ∠ COB = 135°. Substitute the two degree measures into the equation and solve for m ∠ COD . Since 135° − 65° = 70°, m ∠ COD = 70°. This measure is less than 90°, so the angle is acute.

Example 3 Using the Angle Addition Postulate

The measure of the large angle, ∠ PMR , is given. m ∠ PMR = 65° And, the measure of one of the two angles that make up ∠ QMR is also given. m ∠ QMR = 38° Since ∠ QMR and ∠ PMQ make up ∠ PMR , use the Angle Addition Postulate to find m ∠ PMQ .

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