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Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Easy

The figure presents line segments A, D and B E intersecting at point C. Line segments A, B and D E together with line segments A, D and B E form two triangles, A, B C and C D E. In triangle A, B C, angle A, measures 20 degrees, angle B measures x degrees, and the measure of angle C is not given. In triangle C D E, angle D measures y degrees, angle E measures 40 degrees, and the measure of angle C is not given. Angle C of triangle A, B C appears to be congruent to angle C of triangle C D E. A note states that the figure is not drawn to scale.

In the figure above, $line segment A, D$ intersects $line segment B E$ at C. If $x equals 100$ , what is the value of y ?

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Explanation

Choice C is correct. It’s given that $x equals 100$ ; 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: $180 degrees minus 100 degrees, minus 20 degrees, equals 60 degrees$ . 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: $180 degrees minus 60 degrees, minus 40 degrees, equals 80 degrees$ . 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.