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What are the numerical measures of each angle in the diagram?

What are the numerical measures of each angle in the diagram?-example-1
User Avdi
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2 Answers

3 votes

Answer:

29 degrees

151 degrees

Explanation:

User IntStarFoo
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5 votes

Answer:

m∠1 = 29° = m∠3

m∠2 = 151° = m∠4

Explanation:

m∠1 = (3x -1)° and m∠3 = (2x + 9)°

Since, ∠1 and ∠2 are vertically opposite angles and we know that vertically opposite angles are always equal

⇒ ∠1 = ∠2

⇒ (3x -1)° = (2x + 9)°

⇒ 3x - 2x = 9 + 1

⇒ x = 10

⇒ m∠1 = 3 × 10 - 1

⇒ m∠1 = 29° = m∠3

Now, m∠2 + m∠3 = 180° ( sum of linear pair is 180° )

⇒ m∠2 = 180° - 29°

⇒ m∠2 = 151°

Also, ∠2 = ∠4 ( Vertically opposite angles are always equal)

⇒ m∠2 = 151° = m∠4

User Meek
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