Task: Select the correct answer and then click Continue.
In the figure above, if ABCD is a parallelogram,
then x =
A key feature in this figure is the line that extends from the
base of the parallelogram. This line is composed of two supplementary
angles; one is marked 50°, and the other is 
ABC.
Together, these angles must equal 180°, the degree measure of
a straight line. Therefore,
ABC measures 180° – 50° = 130°. Now
that we have handled this external angle and obtained this valuable
piece of information, we can deal with the angles of parallelogram
ABCD.
Since ABCD is a parallelogram, AB is parallel
to DC and AD is parallel to BC.
In addition, diagonal AC functions as a transversal in
this figure, cutting both sets of parallel lines at the same angle
and creating sets of equivalent angles. Therefore, we know that
ACB = DAC
= 20°, and BAC
= DCA = x.
There are now two approaches we can use to determine x:
- Adjacent angles of
a parallelogram are supplementary:
- The sum of angles
in a triangle equals 180°:
Choice (B) is correct.
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