By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3
Step-by-step explanation:
The supplementary angles are:
- Two angles their sum is 180°
- The supplement of an acute angle is an obtuse angle and vice versa
- The supplement of a right angle is a right angle
- If one angle is supplement to two other angles, then the two angles are equal in measure (if 50° is supplement to angles X and Y, then X and y must be 130°)
- Supplement angles of congruent angles are congruent (If angles X and Y are supplement to angles A , B and angles A , B are congruent, then angles X and Y are congruent
∵ ∠1 and ∠2 are supplementary
∴ m∠1 + m∠2 = 180° ⇒ (1)
∵ ∠3 and ∠4 are supplementary
∴ m∠3 + m∠4 = 180° ⇒ (2)
We can equate the left hand sides of (1) and (2) because the right hand sides are equal
∴ m∠1 + m∠2 = m∠3 + m∠4 ⇒ (3)
∵ ∠1 ≅ ∠4
∴ m∠1 = m∠4
- Substitute m∠4 by m∠1 in (3)
∴ m∠1 + m∠2 = m∠3 + m∠1
- Subtract m∠1 from both sides
∴ m∠2 = m∠3
∴ ∠2 ≅ ∠3
By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3
Learn more:
You can learn more about supplementary angles in brainly.com/question/10483199
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