Question

find the value of ( x ). note that, in the image below, ( moverarc{ad} = 141^circ ) and ( moverarc{bd} = 51^circ ).

Explanation:

Step1: Recall secant angle theorem

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs. The formula is:
$$x = \frac{1}{2}(m\overset{\frown}{AD} - m\overset{\frown}{BD})$$

Step2: Substitute given values

Plug $m\overset{\frown}{AD}=141^\circ$ and $m\overset{\frown}{BD}=51^\circ$ into the formula.
$$x = \frac{1}{2}(141^\circ - 51^\circ)$$

Step3: Calculate the difference

Compute the value inside the parentheses first.
$$141^\circ - 51^\circ = 90^\circ$$

Step4: Compute final value

Take half of the resulting difference.
$$x = \frac{1}{2} \times 90^\circ = 45^\circ$$

Answer:

$45^\circ$