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Angle Addition Postulate

Angle Addition Postulate. o. ALGEBRA Given that m LKN =145 , find m LKM and m MKN. STEP 1. Write and solve an equation to find the value of x. m LKN = m LKM + m MKN. o. o. o. 145 = (2 x + 10) + (4 x – 3). EXAMPLE 3. Find angle measures. SOLUTION.

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Angle Addition Postulate

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  1. Angle Addition Postulate

  2. o ALGEBRAGiven that m LKN =145 , find m LKM andm MKN. STEP 1 Write and solve an equation to find the value of x. mLKN = m LKM + mMKN o o o 145 = (2x + 10)+ (4x – 3) EXAMPLE 3 Find angle measures SOLUTION Angle Addition Postulate Substitute angle measures. 145 = 6x + 7 Combine like terms. 138 = 6x Subtract 7 from each side. 23 = x Divide each side by 6.

  3. STEP 2 Evaluate the given expressions when x = 23. mLKM = (2x+ 10)° = (2 23+ 10)° = 56° mMKN = (4x– 3)° = (4 23– 3)° = 89° So, m LKM = 56°and m MKN = 89°. ANSWER EXAMPLE 3 Find angle measures

  4. Find the indicated angle measures. 3. Given that KLMis a straight angle, find mKLN andm NLM. ANSWER 125°, 55° for Example 3 GUIDED PRACTICE

  5. 4. Given that EFGis a right angle, find mEFH andm HFG. ANSWER 60°, 30° for Example 3 GUIDED PRACTICE

  6. Definition Congruent Angles: Two angles are contruent angles if they have the same measure.

  7. Trapeze The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m DEG = 157° ,what is m GKL? SOLUTION There are two pairs of congruent angles: DEF JKL and DEG GKL. Because ∠ DEG GKL, DEG = mGKL. So, mGKL = 157°. ~ ~ ~ EXAMPLE 4 Identify congruent angles

  8. Use the diagram shown. ANSWER T and S, P and R. for Example 4 GUIDED PRACTICE 5. Identify all pairs of congruent angles in the diagram.

  9. Use the diagram shown. o o 6. In the diagram, mPQR = 130 , mQRS = 84, and m TSR = 121 . Find the other angle measures in the diagram. o m PTS = 121°, m QPT = 84° ANSWER for Example 4 GUIDED PRACTICE

  10. Definition Angle Bisector: A ray that divides an angle into two angles that are congruent

  11. 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

  12. ANSWER 90° for Example 5 GUIDED PRACTICE 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.

  13. Homework! • HW: 29: 23-47 odd, 53, 54

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