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Lines X, Y, and Z intersect to form a triangle. If line X is perpendic

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Lines X, Y, and Z intersect to form a triangle. If line X is perpendic  [#permalink]

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New post 25 Feb 2019, 02:38
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Lines X, Y, and Z intersect to form a triangle. If line X is perpendicular to line Y and line X forms a 30-degree angle with line Z, which of the following is the degree measure of the angle formed by the intersection of lines Y and Z?

A. 20°
B. 30°
C. 45°
D. 50°
E. 60°

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Re: Lines X, Y, and Z intersect to form a triangle. If line X is perpendic  [#permalink]

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New post 25 Feb 2019, 04:41
Bunuel wrote:
Lines X, Y, and Z intersect to form a triangle. If line X is perpendicular to line Y and line X forms a 30-degree angle with line Z, which of the following is the degree measure of the angle formed by the intersection of lines Y and Z?

A. 20°
B. 30°
C. 45°
D. 50°
E. 60°


since line y & x are perpendicular so angle 90
angle y & z will be 180-30-90 ; 60
IMO E
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Re: Lines X, Y, and Z intersect to form a triangle. If line X is perpendic  [#permalink]

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New post 25 Feb 2019, 22:48
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Solution


Given:
    • Lines X, Y, and Z intersect to form a rectangle.
    • Line X is perpendicular to line Y.
    • Line X forms a 30° angle with line Z.

To find:
    • The degree measure of the angle formed by the intersection of lines Y and Z

Approach and Working:
As the intersection of lines X, Y, and Z forms a triangle, the 3 angles created by their intersection must sum up to 180°.

Therefore, we can say
    • 90° + 30° + angle between lines Y and Z = 180°
    Or, angle between lines Y and Z = 180° - 120° = 60°

Hence, the correct answer is option E.

Answer: E

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Re: Lines X, Y, and Z intersect to form a triangle. If line X is perpendic   [#permalink] 25 Feb 2019, 22:48
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