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I don't understand this math problem, please help

I don't understand this math problem, please help-example-1
User Hamon
by
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1 Answer

2 votes

Answer/Step-by-step explanation:

1. <A = <B (alternate angles theorem)

90° = 2x (substitution)

Divide both sides by 2

90/2 = 2x/2

45 = x

x = 45

2. <3 = <5 (corresponding angles theorem)

½x = 60 (substitution)

Multiply both sides by 2

x = 60*2

x = 120

3. Based on supplementary bangle theorem, sum of supplementary angles = 180°. Therefore:

m<LFG + m<ABC = 180°

2.5x + x + 33 = 180 (substitution)

Add like terms

3.5x + 33 = 180

3.5x = 180 - 33

3.5x = 147

x = 147/3.5

x = 42

3a. m<LFG = 2.5x

Plug in the value of x

m<LFG = 2.5(42)

m<LFG = 105°

3b. m<ABC = x + 33

Plug in the value of x

m<ABC = 42 + 33

m<ABC = 75°

User Qaisar Nadeem
by
7.7k points

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