Question

question 7 of 10 which equation can be solved to find x, the measure of bd in the diagram a. x - 53 = 233 b. 1/2(233 + x) = 53 c. 1/2(233 - x) = 53 d. x + 53 = 233

Explanation:

Step1: Recall angle - arc relationship

The measure of an angle formed by two secants is half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The larger intercepted arc is $233^{\circ}$ and the smaller intercepted arc is $x$.

Step3: Write the formula

The measure of $\angle C$ is given by $\frac{1}{2}(233 - x)$. Since $\angle C = 53^{\circ}$, the equation is $\frac{1}{2}(233 - x)=53$.

Answer:

C. $\frac{1}{2}(233 - x)=53$