Question

can someone help me with this math problem and find 2 methods to do this

Answer 1

There are two methods for solving for x.

Method 1:

But

Therefore,

The sketch of this is shown below:

Notice that ACB forms a triangle. And we know that the sum of angles in a triangle is 180 degrees.

The angles of the triangle are:

x, 2x and 90

Therefore, we can find x using the theorem referred to above:

$\begin{gathered} x+2x+90=180\text{ (sum of angles in a triangle)} \\ 3x+90=180\text{ (Subtract 90 from both sides)} \\ 3x=180-90 \\ 3x=90\text{ (Divide both sides by 3)} \\ \\ x=\frac{90}{3} \\ x=30 \end{gathered}$

Therefore, x = 30

Method 2:

The sketch of this is shown below:

Now that we have established this, we can apply the theorem that states that the sum of angles on a straight line is 180 degrees.

Thus, we can compute the value of x:

$\begin{gathered} 90+x+2x=180^0 \\ 90+3x=180 \\ \text{subtract 90 from both sides} \\ 3x=180-90 \\ 3x=90\text{ (divide both sides by 3)} \\ x=\frac{90}{3} \\ \\ \therefore x=30 \end{gathered}$

The answer is x = 30