3-2: Angles and Parallel Lines

3-2: Angles and Parallel Lines

Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent.

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In the figure,

 $m\angle5\ =\ 72$ .
Find the measure of  $\angle4$  .

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In the figure,

 $m\angle5\ =\ 72$ .
Find the measure of  $\angle2$  .

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In the figure, suppose the

 $m\angle\ 8=\ 105$ .
Find the measure of  $\angle1$  .

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In the figure, suppose the

 $m\angle\ 8=\ 105$ .
Find the measure of  $\angle2$  .

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In the figure, suppose the

 $m\angle8\ =\ 105$ .
Find the measure of  $\angle3$  .

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.

Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then each pair of exterior angles is congruent.

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Redding Lane and Creek Road are parallel streets that intersect Park Road along the west side of Wendell Park. If

 $m\angle1$  is 118 $\degree,$ find  $m\angle2.$  

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If

 $m\angle1\ =\ 100\degree,$  find  $m\angle4.$  

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If

 $m\angle3\ =\ 70\degree,$  find  $m\angle4.$  

If 

 $m\angle4\ =\ 2x-17$  and  $m\angle1\ =\ 85,$  find  $x.$  

Find   $y$  if 

 $m\angle3\ =\ 4y+30$  and  $m\angle7\ =\ 7y+6.$  

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If

 $m\angle2=4x+7$  and  $m\angle7=5x-13,$  find x.

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Find  $y$  if

 $m\angle5=68$  and  $m\angle3=3y-2.$