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Lines, angles, and triangles SAT question
Math · Geometry and Trigonometry · Easy · Answer it here, explanation included.
In the figure, three lines intersect at point P. If 
and 
, what is the value of z ?
ExplanationShow
Choice C is correct. The angle that is shown as lying between the y° angle and the z° angle is a vertical angle with the x° angle. Since vertical angles are congruent and , the angle between the y° angle and the z° angle measures 65°. Since the 65° angle, the y° angle, and the z° angle are adjacent and form a straight angle, it follows that the sum of the measures of these three angles is 180°, which is represented by the equation 
. It’s given that y = 75. Substituting 75 for y yields 
, which can be rewritten as 
. Subtracting 140° from both sides of this equation yields 
. Therefore, 
.
Choice A is incorrect and may result from finding the value of 
rather than z. Choices B and D are incorrect and may result from conceptual or computational errors.
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