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4 years ago

For lines c, d, and e.

Mathematics

1 answer:

USPshnik [31]4 years ago

5 0

Answer:

A) x = 6

B) ∠3 = 29°

C) ∠1 = 29°

D) ∠2 = 151°

Step-by-step explanation:

Given line e // line d and line c is transversal

Part A: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find x

∠3 = ∠5 because alternate angles are congruent.

So, 5x - 1 = 3x + 11 Combine like terms

5x - 3x = 11 + 1

2x = 12

x = 6

Part B: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find ∠3

∠3 = ∠5 because alternate angles are congruent.

So, 5x - 1 = 3x + 11 Combine like terms

5x - 3x = 11 + 1

2x = 12

x = 6

∴ ∠3 = 5x - 1 = 5 * 6 - 1 =30 - 1 = 29°

Part C: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find ∠1

∠3 = ∠1 because vertically opposite angles are congruent

∠3 = 29°

∴∠1 = 29°

Part D: If ∠3 = 5x-1 and ∠5 = 3x + 11 , find ∠2

The angles 2 and 3 are supplementary angles.

∠3 = 29°

∠2 + ∠3 = 180°

∠2 = 180° - ∠3 = 180° - 29° = 151°

∴ ∠2 = 151°

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