Question

For trapezoid $ABCD$ shown below, $\overline{AB}\parallel \overline{DC}$, the measures of the interior angles are distinct, and the measure of $\angle D$ is $x^{\circ }$. What is the degree measure of $\angle A$ in terms of $x$?

• A. ${(180-x)}^{\circ }$
• B. ${(180-0.5x)}^{\circ }$
• C. ${(180+0.5x)}^{\circ }$
• D. ${(180+x)}^{\circ }$
• E. $x^{\circ }$

Answer 1

Answer: (A)

${(180-x)}^{\circ }$

In given figure quadrilateral ABCD is trapezoid.

AB $\parallel$ DC [Given]

So, $\angle$A + $\angle$D = 180${}^{\circ }$ [ Consecutive angles between parallel sides are supplementary ]

We have been given that, $\angle$D = $x^{\circ }$

So, $\angle A+x^{\circ }={180}^{\circ }$

$\therefore$ $\angle$$A$ = $(180-x{)}^{\circ }$