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Can someone help me with this geometry question with vertex angles?

Can someone help me with this geometry question with vertex angles?-example-1

1 Answer

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Answer:

∠ 3 = 93°

Explanation:

∠ 1 and ∠ 2 are vertically opposite angles and are congruent ( equal ), so

∠ 1 = ∠ 2 ( substitute values )

2x - 3 = x + 42 ( subtract x from both sides )

x - 3 = 42 ( add 3 to both sides )

x = 45

Then

∠ 1 = 2x - 3 = 2(45) - 3 = 90 - 3 = 87°

∠ 1 and ∠ 3 are a linear pair and sum to 180° , that is

∠ 1 + ∠ 3 = 180° ( substitute ∠ 1 = 87° )

87° + ∠ 3 = 180° ( subtract 87° from both sides )

∠ 3 = 93°

User Nayfe
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