In the figure above, `bar(AD)` intersects `bar(BE)` at C. If x = 100, what is the value of y ?

Options

A. 100
B. 90
C. 80
D. 60

Answer

C

Explanation

It’s given that x = 100, 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: `180^@ − 100^@ − 20^@ = 60^@`. 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: `180^@ − 60^@ − 40^@ = 80^@`. 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.