x= 26°
STEP - BY - STEP EXPLANATION
What to find?
The value of x.
I will first need to sketch and then name the points for better understanding.
To solve, we can simply use the formula;
[tex]x=\frac{1}{2}(\text{arcCD - arc AB)}[/tex]
Observe that we only have the value for arc CD =116°
This implies that we need to obtain the value for arc AB to be able to put the formula into use.
From the diagram, given that the chord passes through the center makes it a diameter.
Hence, the circumference BC = 180°
To obtain the value of arc AB, simply subtract 116° from 180°.
That is;
arc AB = 180° - 116° = 64°
We can now proceed to calculate the value of x using the formua above.
Substitute the values into the formula and simplify.
[tex]x=\frac{1}{2}(116-64)[/tex][tex]=\frac{52}{2}[/tex]
= 26°
Therefore, x= 26°
