Question

n the trapezoid below, if < BAC = 3x - 5 degrees and the measure of < DCA is 6x - 4 degrees, find x.

Answer 1

ANSWER

$x=21$

Option A

EXPLANATION

Recall, that the adjacent angles of a trapezoid add up to 180.

Hence;

$\angle BAC+\angle DCA=180$

Given;

$\begin{gathered} \angle BAC=3x+5 \\ \angle DCA=6x-4 \end{gathered}$

Now, let the sum of the angles be equal to 180.

$3x-5+(6x-4)=180$

Solving by collecting like terms;

$\begin{gathered} 3x-5+6x-4=180 \\ 3x+6x-5-4=180 \\ 9x-9=180 \\ 9x=180-9 \\ 9x=189 \end{gathered}$

Divide both sides by 9

$\begin{gathered} 9x=189 \\ \frac{9x}{9}=\frac{189}{9} \\ x=21 \end{gathered}$