2 Answers

Davmos · Answer 1 · 2021-10-07T21:39:13+0000

The Question is Incomplete, the Complete Question is with figure is below.

Answer:

Therefore,

The Measure of angle 6 is

$\angle 6 =45\°$

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

$\angle 1 + \angle 3 = 180\°$

Substituting the values we get

$135 + \angle 3 = 180\\\\\angle 3 = 180-135=45\°$

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

$\angle 3 = \angle 6$

But
$\angle 3 =45\°$

$\angle 6 =45\°$ ...Transitive Property

Therefore,

The Measure of angle 6 is

$\angle 6 =45\°$

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