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Lines, angles, and triangles SAT question

Math · Geometry and Trigonometry · Easy · Answer it here, explanation included.

In the figure above, lines $l$ and m are parallel, $y equals 20$ , and $z equals 60$ . What is the value of x ?

ExplanationShow

Choice B is correct. Let the measure of the third angle in the smaller triangle be $a, degrees$ . Since lines $l$ and m are parallel and cut by transversals, it follows that the corresponding angles formed are congruent. So $a degrees, equals y degrees, which equals 20 degrees$ . The sum of the measures of the interior angles of a triangle is $180 degrees$ , which for the interior angles in the smaller triangle yields $a, plus x, plus z, equals 180$ . Given that $z equals 60$ and $a, equals 20$ , it follows that $20 plus x, plus 60, equals 180$ . Solving for x gives $x equals, 180 minus 60, minus 20$ , or $x equals 100$ .

Choice A is incorrect and may result from incorrectly assuming that angles $x plus z, equals 180$ . Choice C is incorrect and may result from incorrectly assuming that the smaller triangle is a right triangle, with x as the right angle. Choice D is incorrect and may result from a misunderstanding of the exterior angle theorem and incorrectly assuming that $x equals, y plus z$ .

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Lines, angles, and triangles SAT question

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