Question

in circle a, mbc⌢ is 67° and mef⌢ is 74°. what is m∠fde?

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arcs

The inscribed angle $\angle FDE$ intercepts arcs $\overset{\frown}{EF}$ and $\overset{\frown}{BC}$.

Step3: Use the formula for the measure of an inscribed - angle formed by two chords

The measure of $\angle FDE=\frac{1}{2}(\overset{\frown}{EF}-\overset{\frown}{BC})$.

Step4: Substitute the given arc - measures

We know that $\overset{\frown}{EF} = 74^{\circ}$ and $\overset{\frown}{BC}=67^{\circ}$. Then $\angle FDE=\frac{1}{2}(74 - 67)$.

Step5: Calculate the value of the angle

$\frac{1}{2}(74 - 67)=\frac{1}{2}\times7 = 3.5^{\circ}$.

Answer:

$3.5^{\circ}$