Let measure of angle 6=x. Which angles have the measure of 180-x?

Question 1

Question 2

Answer:

$\large\textsf{See below.}$

Explanation:

$\textsf{We are asked which angles are equal to 180}^(\circ) \textsf{- x.}$

$\textsf{We should look at m} \angle 6 \ \textsf{as it's equal to x.}$

$\textsf{Note that m} \tt \angle 6 \ \textsf{is formed by Perpendicular Lines.}$

$\large\underline{\textsf{What are Perpendicular Lines?}}$

$\textsf{Perpendicular Lines are \underline{2 lines} that are \underline{opposite slopes}; They \underline{intersect} each other.}$

$\textsf{Because Perpendicular Lines are opposite, they form \underline{4} 90}^(\circ) \ \textsf{angles.}$

$\large\underline{\textsf{We can identify that;}}$

$\tt m \angle 6 = 90^(\circ).$

$\textsf{Remember that we are asked for angles equal to the difference of 180}^(\circ) \ \textsf{and} \ \tt m \angle 6.$

$\large\underline{\textsf{Substitute;}}$

$\tt 180^(\circ) - 90^(\circ) = 90^(\circ).$

$\textsf{We are asked for angles with the same measure.}$

$\textsf{Remember that Perpendicular Angles equal 90}^(\circ).$

$\textsf{This means that Angles 5, 7, 8, 9, 10, 11, and 12 have the measure of 90}^(\circ).$

$\large\underline{\textsf{Hence;}}$

$\Large\boxed{\tt \angle 5, \angle 7, \angle 8, \angle 9, \angle 10, \angle 11, and \ \angle 12 \ equal \ 180^(\circ) - m\angle 6.}$

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