EXAMPLE 3 Find angle measures ALGEBRA Given that

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

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

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

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

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

GUIDED PRACTICE for Example 3 STEP 2 Evaluate the given expressions when x = 29. m EFH = (2 x + 2)° = (2 29 +2)° = 60° m HFG = (x + 1)° = (29 + 1)° = 30° ANSWER m EFG = 60° m HFG = 30°