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5 7 8 6 Lines j and k are parallel. m3= (3x-18)° and m 4= (y + 25)° and m 7-75°. Find the values of x and y.​

5 7 8 6 Lines j and k are parallel. m3= (3x-18)° and m 4= (y + 25)° and m 7-75°. Find-example-1
User Servet
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1 Answer

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Explanation:

when 2 lines intersect, then the 2 angles on top are the same as the 2 angles below the intersection - just left-right mirrored.

and the sum of both intersection angles on one side of a line are together 180° (because one side of such a line is representing a half-circle around the intersection point).

and when parallel lines are intersected by the same line, then all 4 angles at one intersection point are the same as the 4 angles at the other intersection points. otherwise the lines are not parallel.

so,

angle 1 = angle 4 = angle 5 = angle 8

angle 2 = angle 3 = angle 6 = angle 7

angle 1 + angle 2 = angle 2 + angle 4 =

= angle 3 + angle 4 =

= angle 3 + angle 1 = 180°

angle 5 + angle 6 = angle 6 + angle 8 =

= angle 8 + angle 7 =

= angle 7 + angle 5 = 180°

we know angle 7 = 75°.

therefore,

angle 2 = angle 3 = angle 6 = 75°

therefore,

3x -18 = 75

3x = 93

x = 31

angle 4 + angle 3 = angle 4 + 75 = 180°

angle 4 = 105°

y + 25 = 105

y = 80

User David Callanan
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