Question

In the trapezoid below, if < BAC = 3x - 4 degrees and the measure of < DCA is 2x + 9 degrees, find x

Answer 1

b. 35

Explanation:

We can determine the value of x, knowing that the sum of all the angles of the trapezoid is equal to 360°.

Also that the upper angles are equal and the lower angles are equal, therefore, we can establish the following equation:

`\begin{gathered} 2\cdot\angle BAC+2\cdot\angle DCA=360 \\ \\ \text{ We replacing:} \\ \\ 2\cdot \left(3x-4\right)+2\cdot \left(2x+9\right)=360 \\ \\ 6x-8+4x+18=360 \\ \\ 10x+10=360 \\ \\ 10x=360-10 \\ \\ x=(350)/(10) \\ \\ x=35 \end{gathered}`

Therefore, the correct answer is b. 35