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EXAMPLE 3

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. Angle Addition Postulate.

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EXAMPLE 3

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  1. 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.

  2. 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

  3. 3. Given that KLMis straight angle, find mKLN andm NLM. STEP 1 Write and solve an equation to find the value of x. m KLM + m NLM = 180° (10x – 5)° + (4x +3)° = 180° = 180 14x – 2 = 182 14x x = 13 for Example 3 GUIDED PRACTICE Find the indicated angle measures. SOLUTION Straight angle Substitute angle measures. Combine like terms. Subtract 2 from each side. Divide each side by 14.

  4. STEP 2 Evaluate the given expressions when x = 13. mKLM = (10x– 5)° = (10 13– 5)° = 125° mNLM = (4x+ 3)° = (4 13+ 3)° = 55° mKLM = 125° mNLM = 55° ANSWER for Example 3 GUIDED PRACTICE

  5. STEP 1 Write and solve an equation to find the value of x. m EFG + m HFG m EFG EFG is a right angle = = 90° (2x + 2)° + (x +1)° = 90° = 90 3x + 3 = 87 3x x = 29 for Example 3 GUIDED PRACTICE 4. Given that EFGis a right angle, find mEFH andm HFG. SOLUTION Substitute angle measures. Combine like terms. Subtract 3 from each side. Divide each side by 3.

  6. STEP 2 Evaluate the given expressions when x = 29. mEFH = (2x+ 2)° = (2 29 +2)° = 60° mHFG = (x+ 1)° = (29+ 1)° = 30° mEFG = 60° mHFG = 30° ANSWER for Example 3 GUIDED PRACTICE

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