Question

find m∠ejf. drag the expressions into the boxes to correctly complete the solution. show hints m∠ejf = = = =

Explanation:

Step1: Recall angle - arc relationship

The measure of an angle formed by two secants intersecting outside a circle is half the positive difference of the measures of the intercepted arcs. Let the larger arc be $m\overset{\frown}{EF}=140^{\circ}$ and the smaller arc be $m\overset{\frown}{HG} = 36^{\circ}$.

Step2: Apply the formula

The formula for the measure of the angle $\angle EJF$ formed by two secants is $m\angle EJF=\frac{1}{2}(m\overset{\frown}{EF}-m\overset{\frown}{HG})$.
Substitute the values of the arcs: $m\angle EJF=\frac{1}{2}(140 - 36)$.
First, calculate the difference inside the parentheses: $140-36 = 104$.
Then, multiply by $\frac{1}{2}$: $\frac{1}{2}\times104 = 52$.

Answer:

$52^{\circ}$