Question

question 7 of 10
what is the measure of shown in the diagram below?
a. 59.5°
b. 49°
c. 24.5°
d. 14°

Explanation:

Step1: Recall the formula for the measure of an angle formed outside the circle

The measure of an angle formed outside the circle is $\frac{1}{2}$ (difference of the measures of the intercepted arcs). The formula is $m\angle Y=\frac{1}{2}(m\overset{\frown}{VW}-m\overset{\frown}{XZ})$.

Step2: Substitute the known values

We know that $m\angle Y = 25^{\circ}$ and $m\overset{\frown}{VW}=84^{\circ}$. Let $m\overset{\frown}{XZ}=x$. Then $25=\frac{1}{2}(84 - x)$.

Step3: Solve the equation

Multiply both sides of the equation by 2: $25\times2=84 - x$. So, $50 = 84 - x$. Then $x=84 - 50$.

Answer:

B. $49^{\circ}$