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Lines, angles, and triangles SAT question
Math · Geometry and Trigonometry · Easy · Answer it here, explanation included.
In the figure above, 
intersects 
at C. If 
, what is the value of y ?
ExplanationShow
Choice C is correct. It’s given that ; therefore, substituting 100 for x in triangle ABC gives two known angle measures for this triangle. The sum of the measures of the interior angles of any triangle equals 180°. Subtracting the two known angle measures of triangle ABC from 180° gives the third angle measure: 
. This is the measure of angle BCA. Since vertical angles are congruent, the measure of angle DCE is also 60°. Subtracting the two known angle measures of triangle CDE from 180° gives the third angle measure: 
. Therefore, the value of y is 80.
Choice A is incorrect and may result from a calculation error. Choice B is incorrect and may result from classifying angle CDE as a right angle. Choice D is incorrect and may result from finding the measure of angle BCA or DCE instead of the measure of angle CDE.
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