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

In triangle ABC, the measure of angle A is $50 degrees$ . If triangle ABC is isosceles, which of the following is NOT a possible measure of angle B ?

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Explanation

Choice D is correct. The sum of the three interior angles in a triangle is $180 degrees$ . It’s given that angle A measures $50 degrees$ . If angle B measured $100 degrees$ , the measure of angle C would be $180 degrees minus, open parenthesis, 50 degrees plus 100 degrees, close parenthesis, equals 30 degrees$ . Thus, the measures of the angles in the triangle would be $50 degrees$ , $100 degrees$ , and $30 degrees$ . However, an isosceles triangle has two angles of equal measure. Therefore, angle B can’t measure $100 degrees$ .

Choice A is incorrect. If angle B has measure $50 degrees$ , then angle C would measure $180 degrees minus, open parenthesis, 50 degrees plus 50 degrees, close parenthesis, equals 80 degrees$ , and $50 degrees$ , $50 degrees$ , and $80 degrees$ could be the angle measures of an isosceles triangle. Choice B is incorrect. If angle B has measure $65 degrees$ , then angle C would measure $180 degrees minus, open parenthesis, 65 degrees plus 50 degrees, close parenthesis, equals 65 degrees$ , and $50 degrees$ , $65 degrees$ , and $65 degrees$ could be the angle measures of an isosceles triangle. Choice C is incorrect. If angle B has measure $80 degrees$ , then angle C would measure $180 degrees minus, open parenthesis, 80 degrees plus 50 degrees, close parenthesis, equals 50 degrees$ , and $50 degrees$ , $80 degrees$ , and $50 degrees$ could be the angle measures of an isosceles triangle.