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Lines, angles, and triangles SAT question
Math · Geometry and Trigonometry · Easy · Answer it here, explanation included.
In the given figure, 
extends to point D. If the measure of 
is equal to the measure of 
, what is the value of x ?
ExplanationShow
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.
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