Question

what is the measure of bd shown in the diagram below? a. 33° b. 66° c. 36° d. 63°

Explanation:

Step1: Recall the secant - secant angle formula

The measure of an angle formed by two secants intersecting outside a circle is given by $\frac{1}{2}(\text{major arc}-\text{minor arc})$. Let the measure of arc $BD=x$ and the measure of arc $AE = 96^{\circ}$. The angle $\angle C = 30^{\circ}$.

Step2: Apply the formula

We know that $\angle C=\frac{1}{2}(96 - x)$. Since $\angle C = 30^{\circ}$, we have the equation $30=\frac{1}{2}(96 - x)$.

Step3: Solve the equation

Multiply both sides of the equation by 2: $60=96 - x$. Then, add $x$ to both sides: $x + 60=96$. Subtract 60 from both sides: $x=96 - 60=36^{\circ}$. So the measure of arc $BD$ is $36^{\circ}$.

Answer:

C. 36°