Answer to Question #174176 in Geometry for Avanthika

Question #174176

I and m are two parallel lines. <2 -75°, find the measure of all other angles.


1
Expert's answer
2021-03-31T14:10:03-0400

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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