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∠3 and ∠6 are alternate interior angles. If m∠3 = 75, what is the measure of ∠6? *

15°
75°
105°
180°

Sagot :

VibingLegend27idn

Answer:

Correct Answer: 75°

Yadaohonieidn

75°

Given as l and m are two parallel lines, angle 2=75 degrees.

Let P is a transversal line to make angles on Parallel lines as l and m.

For

  • From the figure, m⟨1 and m⟨2 are supplementary angles,

  • m⟨1+ m⟨2=180 degrees
  • m⟨1+ 75 degrees=180 degrees
  • m⟨1=105 degrees

For m⟨3

  • From the figure,

  • m⟨1= m⟨3
  • m⟨3= 105 degrees

For m⟨4

  • From the figure, m⟨2 and m⟨4 are vertically opposite angles,

  • m⟨2= m⟨4
  • m⟨4= 75 degrees

For m⟨5

  • From the figure, m⟨3 and m⟨5 are alternate interior angles,

  • m⟨3= m⟨5
  • m⟨5= 105 degrees

For m⟨6

  • From the figure, m⟨2 and m⟨6 are corresponding angles,

  • m⟨2= m⟨6
  • m⟨6= 75 degrees

For m⟨7

  • From the figure, m⟨7 and m⟨3 are corresponding angles,

  • m⟨3= m⟨7
  • m⟨7= 105 degrees

For m⟨8

  • From the figure, m⟨6 and m⟨8 are vertically opposite angles,

  • m⟨6= m⟨8
  • m⟨8= 75 degrees

Summary:

  • m⟨1=105 degrees
  • m⟨3= 105 degrees
  • m⟨4= 75 degrees
  • m⟨5= 105 degrees
  • m⟨6= 75 degrees
  • m⟨7= 105 degrees
  • m⟨8= 75 degrees
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