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3 years ago

Please help me with this question

Mathematics

1 answer:

BartSMP [9]3 years ago

4 0

Answer:

$3x-28=2x+25\\x=53$

Step-by-step explanation:

Parallel lines cut by a transversal are two lines which do not cross intersected by a third line. Because lines such as m and n are parallel, we have angles which are equal to each other.

Corresponding Angles - angles located in the same position in each intersection. Can be shown by translating or sliding the angle down/up.
Alternate Interior Angles - angles located inside the parallel lines across the transversal. Can be shown by reflecting and translating or rotation.
Alternate Exterior Angles - angles located outside the parallel lines across the transversal. Can be shown by reflecting and translating or rotation.

Vertical angles - angles across a vertex from one another. Can be shown by reflection.

The angles shown here are located outside the parallel lines and across the transversal from each other. Therefore we have Alternate Exteroir angles and can set them equal to each other to solve for x.

$3x-28=2x+25\\3x-2x-28=2x-2x+25\\x-28=25\\x-28+28=25+28\\x=53$

We check our work and should get equal angles:

$3(53)-28=2(53)+25\\159-28=106+25\\131=131$

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