In the figure above, lines and m are parallel,
, and
. What is the value of x ?
Correct answer: B
Explanation
Choice B is correct. Let the measure of the third angle in the smaller triangle be . Since lines
and m are parallel and cut by transversals, it follows that the corresponding angles formed are congruent. So
. The sum of the measures of the interior angles of a triangle is
, which for the interior angles in the smaller triangle yields
. Given that
and
, it follows that
. Solving for x gives
, or
.
Choice A is incorrect and may result from incorrectly assuming that angles . 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
.
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