In the given figure, extends to point D. If the measure of
is equal to the measure of
, what is the value of x ?
Correct answer: D
Explanation
Choice D is correct. Since and
form a linear pair of angles, their measures sum to 180°. It’s given that the measure of
is 110°. Therefore,
. Subtracting 110° from both sides of this equation gives the measure of
as 70°. It’s also given that the measure of
is equal to the measure of
. Thus, the measure of
is also 70°. The measures of the interior angles of a triangle sum to 180°. Thus,
. Combining like terms on the left-hand side of this equation yields
. Subtracting 140° from both sides of this equation yields
, or
.
Choice A is incorrect. This is the value of the measure of . Choice B is incorrect. This is the value of the measure of each of the other two interior angles,
and
. Choice C is incorrect and may result from an error made when identifying the relationship between the exterior angle of a triangle and the interior angles of the triangle.
Loading…
Searched on YouTube by topic, not by question text. Open this search on YouTube →
SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.