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

N The Trapezoid Below If Lt BAC 3x 5 Degrees And The Measure Of Lt DCA Is 6x 4 Degrees Find X class=

Sagot :

ANSWER

[tex]x=21[/tex]

Option A

EXPLANATION

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

Hence;

[tex]\angle BAC+\angle DCA=180[/tex]

Given;

[tex]\begin{gathered} \angle BAC=3x+5 \\ \angle DCA=6x-4 \end{gathered}[/tex]

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

[tex]3x-5+(6x-4)=180[/tex]

Solving by collecting like terms;

[tex]\begin{gathered} 3x-5+6x-4=180 \\ 3x+6x-5-4=180 \\ 9x-9=180 \\ 9x=180-9 \\ 9x=189 \end{gathered}[/tex]

Divide both sides by 9

[tex]\begin{gathered} 9x=189 \\ \frac{9x}{9}=\frac{189}{9} \\ x=21 \end{gathered}[/tex]

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