I’d very much appreciate some help!I was tested on this question and didn’t know how to solve it much, this is new material for me. I need a step by step tutorial with reasons! Thank you!

Id very much appreciate some helpI was tested on this question and didnt know how to solve it much this is new material for me I need a step by step tutorial wi class=

Respuesta :

Answer:

The value of x is;

[tex]x=4[/tex]

Explanation:

From the question, it was stated that line BD bisects(divide into two equal halves) angle ABC.

So, angle ABD will be the same as angle CBD.

[tex]\measuredangle ABD=\measuredangle CBD[/tex]

Given;

[tex]\begin{gathered} m\measuredangle ABD=7x-10 \\ m\measuredangle CBD=4x+2 \end{gathered}[/tex]

substituting the given values we have;

[tex]\begin{gathered} \measuredangle ABD=\measuredangle CBD \\ 7x-10=4x+2 \end{gathered}[/tex]

Solving the resulting equation for x, we have;

[tex]\begin{gathered} 7x-10=4x+2 \\ \text{add 10 to both sides;} \\ 7x-10+10=4x+2+10 \\ 7x=4x+12 \\ \text{subtract 4x from both sides} \\ 7x-4x=4x-4x+12 \\ 3x=12 \\ \text{divide both sides by 3} \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]

Therefore, the value of x is;

[tex]x=4[/tex]

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