Question

question 7 (multiple choice worth 1 points)
(07.01 mc)
in circle a, mbc is 67° and mef is 74°.
what is m∠fde?
o 37°
o 74°
o 70.5°
o 33.5°

Explanation:

Step1: Recall the formula for the measure of an angle formed by two chords

The measure of an angle formed by two chords intersecting inside a circle is $\frac{1}{2}$ the sum of the measures of the intercepted arcs. So, $m\angle FDE=\frac{1}{2}(m\overset{\frown}{EF}+m\overset{\frown}{BC})$.

Step2: Substitute the given arc measures

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

Step3: Calculate the sum inside the parentheses

First, find $74+67 = 141$.

Step4: Divide by 2

Now, $\frac{1}{2}\times141 = 70.5$.

Answer:

$70.5^{\circ}$