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Angle Bisector Theorem: Find Angle Measurement using Angle Addition Postulate

Learn how to find angle measurements using the Angle Addition Postulate when an angle is bisected. Step-by-step examples provided.

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Angle Bisector Theorem: Find Angle Measurement using Angle Addition Postulate

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  1. In the diagram at the right, YWbisects XYZ, and mXYW = 18. Find m XYZ. o By the Angle Addition Postulate, m XYZ =mXYW + m WYZ. BecauseYW bisects XYZyou know thatXYW WYZ. So, m XYW = m WYZ, and you can write M XYZ = m XYW + m WYZ = 18° + 18° = 36°. ~ EXAMPLE 5 Double an angle measure SOLUTION

  2. 7. Angle MNPis a straight angle, and NQbisects MNP. Draw MNP And NQ. Use arcs to mark the congruent angles in your diagram, and give the angle measures of these congruent angles. SOLUTION for Example 5 GUIDED PRACTICE

  3. 2 m MNQ = 180° = 90° m MNQ = mPNQ m MNQ + mPNQ m MNQ + mPNQ = 180° = 180° The solution is = 90° m MNQ = mPNQ m MNQ + mMNQ m MNQ for Example 5 GUIDED PRACTICE Angle addition postulate Straight angle Add Divided each side by 2

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