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Answer:
Step-by-step explanation:
Given a transversal that intersects a set of parallel lines, various angles are formed.
When given this situation in geometry, these angles have different names and statements (primarily theorems) which justify their relationship.
There are 8 primary types of possible angles of parallel lines including:
- Alternate Interior
- Alternate Exterior
- Same-Side (Consecutive) Interior
- Same-Side (Consecutive) Exterior
- Corresponding Angles
- Vertical Angles
- Supplementary Angles
- Linear Pair
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According to what is given in the problem, we know that:
m∠3 = 135°.
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To solve for m∠7, we must identify the relationship that ∠3 and ∠7 have.
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Here is the solution in proof form:
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Statement | Reason
m∠3 = 135° | Given
m∠3 ≅ m∠5 | Vertical Angles
m∠5 ≅ m∠7 | Corresponding Angles Theorem
m∠3 ≅ m∠7 | Transitive Property of Equality
m∠7 = 135° | Definition of Congruent Angles