Question

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

Answer 1

`x=21`

Option A

Step-by-step 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 \\ (9x)/(9)=(189)/(9) \\ x=21 \end{gathered}`