EXAMPLE 3 Find angle measures

oALGEBRA Given that m LKN =145 , find m LKM and m MKN.

SOLUTION

STEP 1

Write and solve an equation to find the value of x.

m LKN = m LKM + m MKN Angle Addition Postulate

Substitute angle measures.

145 = 6x + 7 Combine like terms.

Subtract 7 from each side.138 = 6x

Divide each side by 6.23 = x

145 = (2x + 10) + (4x – 3)o oo

EXAMPLE 3 Find angle measures

STEP 2

Evaluate the given expressions when x = 23.

m LKM = (2x + 10)° = (2 23 + 10)° = 56°

m MKN = (4x – 3)° = (4 23 – 3)° = 89°

So, m LKM = 56° and m MKN = 89°.ANSWER

GUIDED PRACTICE for Example 3

Find the indicated angle measures.

3. Given that KLM is straight angle, find m KLN and m NLM.

STEP 1

Write and solve an equation to find the value of x.

Straight angle

Substitute angle measures.

Combine like terms.

Subtract 2 from each side.

Divide each side by 14.

m KLM + m NLM = 180°

(10x – 5)° + (4x +3)°= 180°14x – 2 = 180

14x = 182

x = 13

SOLUTION

GUIDED PRACTICE for Example 3

STEP 2

Evaluate the given expressions when x = 13.

m KLM = (10x – 5)° = (10 13 – 5)° = 125°

m NLM = (4x + 3)° = (4 13 + 3)° = 55°

ANSWER m KLM = 125° m NLM = 55°

GUIDED PRACTICE for Example 3

4. Given that EFG is a right angle, find m EFH and m HFG.

STEP 1

Write and solve an equation to find the value of x.

Substitute angle measures.

Combine like terms.

Subtract 3 from each side.

Divide each side by 3.

m EFG + m HFGm EFG= = 90°

(2x + 2)° + (x +1)° = 90°3x + 3 = 90

3x = 87

x = 29

EFG is a right angle

SOLUTION

GUIDED PRACTICE for Example 3

STEP 2

Evaluate the given expressions when x = 29.

m EFH = (2x + 2)° = (2 29 +2)° = 60°

m HFG = (x + 1)° = (29 + 1)° = 30°

ANSWER m EFG = 60° m HFG = 30°