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Solving for Angle Measures in Geometry Problems Using Algebra

This guide explores solving for unknown angle measures in geometric problems involving straight angles and right angles. It demonstrates how to set up and solve equations to find values of x using the Angle Addition Postulate. Examples include finding m.LKM and m.MKN given m.LKN = 145°; plus step-by-step solutions for other angles. Understanding how to manipulate and solve these equations is crucial for students learning geometry and algebra simultaneously.

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Solving for Angle Measures in Geometry Problems Using Algebra

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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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