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Determine the m ∠5, if m ∠7 = (10x - 30)° and m ∠2 = (5x + 5)°

Determine the m ∠5, if m ∠7 = (10x - 30)° and m ∠2 = (5x + 5)°-example-1

1 Answer

3 votes

Answer:

C

Explanation:

∠ 7 and ∠ 2 are alternate angles and are congruent (equal ) , then

∠ 7 = ∠ 2 ( substitute values )

10x - 30 = 5x + 5 ( subtract 5x from both sides )

5x - 30 = 5 ( add 30 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Then

∠ 7 = 10x - 30 = 10(7) - 30 = 70 - 30 = 40°

∠ 5 and ∠ 7 are a linear pair and sum to 180° , that is

∠ 5 + ∠ 7 = 180°

∠ 5 + 40° = 180° ( subtract 40° from both sides )

∠ 5 = 140°

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