Question

Given m 1 n, find the value of x. m n (4x+8)° 72°

Answer 1

When two parallel lines are cross by a transversal, the formed angles will be:

Angles in blue have the same measure

Angles in green have the same measure

Vertical angles: have the same mesure (1 and 6, 2 and 5, 3 and 8, 4 and 7)

Corresponding angles: have the same measure (1 and 3, 2 and 4, 5 and 7, 6 and 8)

Alternate interior angles: have the same measure (2 and 7, 6 and 3)

Alternate exterior angles: have the same measure (5 and 4, 1 and 8)

Consecutive interior angles: sum 180º (2and 3, 6 and 7)

Consecutive exterior angles: sum 180º (1 and 4, 5 and 8)

One angle in blue and one angle in green are rupplementary, they sum 180º

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You have: two consecutive exterior angles.

Then, the given anlges sum 180º:

`(4x+8)º+72º=180º`

Solve the equation above for x:

`\begin{gathered} 4x+8+72=180 \\ 4x+80=180 \\ 4x=180-80 \\ 4x=100 \\ x=(100)/(4) \\ x=25 \end{gathered}`Then, x is 25