For what value of x is line m parallel to line n?

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x =

Line m is parallel to line n. Line m is above line n. A transversal line cuts both parallel lines. The acute upward left angle made by the transversal line with line m is labeled as 75 degrees. The obtuse downward left angle made by the transversal line with line m is labeled as 105 degrees. The obtuse upward right angle made by the transversal line with line n is labeled as left parenthesis 10 x plus 15 right parenthesis degrees.

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4 June, 18:06

For what value of x is line m parallel to line n?

Enter your answer in the box.

x =

Line m is parallel to line n. Line m is above line n. A transversal line cuts both parallel lines. The acute upward left angle made by the transversal line with line m is labeled as 75 degrees. The obtuse downward left angle made by the transversal line with line m is labeled as 105 degrees. The obtuse upward right angle made by the transversal line with line n is labeled as left parenthesis 10 x plus 15 right parenthesis degrees.

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Kelsey · Answer 1

Refer to the diagram shown below.

Lines m and n are parallel.

Because angles on equivalent sides of a traversal of parallel lines are equal, therefore

m∠y = 75°

Because the sum of angles on one side of a straight line is 180°, therefore

y + (10x + 15) = 180

75 + 10x + 15 = 180

10x + 90 = 180

10x = 180 - 90 = 90

x = 9

Answer: x = 9