Question

I am positive for covid so i don’t have motivation to do this problem. please don’t take too long answering this problem.

Answer 1

Answer:

The measure of arc BED is;

$\hat{\text{mBED}}=225^{\circ}$

Explanation:

Given that line AD and BE are diameters.

And;

$\begin{gathered} \text{mDE}=x+49 \\ \text{mAE}=x+139 \end{gathered}$

We can see from the figure that arc AE and DE sum up to give a semicircle, so they will have a combined angle of 180 degrees.

$\begin{gathered} \text{mAE}+\text{mDE}=180 \\ x+139+x+49=180 \\ 2x+188=180 \\ 2x=180-188 \\ 2x=-8 \\ x=-\frac{8}{2} \\ x=-4 \end{gathered}$

Substituting the values of x;

$\begin{gathered} \text{mDE}=x+49=-4+49 \\ \text{mDE}=45^{\circ} \end{gathered}$$\begin{gathered} \text{mAE}=x+139=-4+139 \\ \text{mAE}=135^{\circ} \end{gathered}$

To get mBED, BE is a straight line so it will be equal to 180.

$\begin{gathered} \hat{\text{mBED}}=\text{mBE}+\text{mDE} \\ \hat{\text{mBED}}=180+45 \\ \hat{\text{mBED}}=225^{\circ} \end{gathered}$

Therefore, the measure of arc BED is;

$\hat{\text{mBED}}=225^{\circ}$