The Question is Incomplete, the Complete Question is with figure is below.
Answer:
Therefore,
The Measure of angle 6 is
[tex]\angle 6 =45\°[/tex]
Step-by-step explanation:
Given:
m∠1 = 135°
Lines b and c are parallel.
To Find:
m∠6 = ?
Solution:
Linear Pair:
A linear pair of angles is formed when two lines intersect.
Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Example
∠ 1 and ∠ 2 ∠ 1 and ∠ 3 ,etc
[tex]\angle 1 + \angle 3 = 180\°[/tex]
Substituting the values we get
[tex]135 + \angle 3 = 180\\\\\angle 3 = 180-135=45\°[/tex]
Now,
Lines b and c are parallel. .Given
When Two lines are Parallel Alternate interior angles are equal
∠ 3 and ∠ 6 are Alternate Interior angles
[tex]\angle 3 = \angle 6[/tex]
But [tex]\angle 3 =45\°[/tex]
[tex]\angle 6 =45\°[/tex] ...Transitive Property
Therefore,
The Measure of angle 6 is
[tex]\angle 6 =45\°[/tex]
