Question

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!

Answer 1

The value of x is;

`x=4`

Step-by-step 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.

`\measuredangle ABD=\measuredangle CBD`

Given;

`\begin{gathered} m\measuredangle ABD=7x-10 \\ m\measuredangle CBD=4x+2 \end{gathered}`

substituting the given values we have;

`\begin{gathered} \measuredangle ABD=\measuredangle CBD \\ 7x-10=4x+2 \end{gathered}`

Solving the resulting equation for x, we have;

`\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} \\ (3x)/(3)=(12)/(3) \\ x=4 \end{gathered}`

Therefore, the value of x is;

`x=4`