Question

" Given m ED= 44 and m< BFC = 35, determine the measure of the arc m BC

A) 79°
B) 89°
C) 99°
D) 109°"

Answer 1

The measure of the arc
`\( \angle BC \) is \( 99^\circ \) (Option C).`

Thus the correct option is C.

Step-by-step explanation:

To determine the measure of arc
`\( \angle BC \),` consider the Angle-Arc Relationship in a circle, which states that the measure of an inscribed angle is equal to half the measure of the intercepted arc.

In this case,
`\( m\angle BFC = (1)/(2)m\angle BC \).`

Given that
`\( m\angle BFC = 35^\circ \),` we can find
`\( m\angle BC \)`by multiplying
`\( 35^\circ \)` by 2, resulting in
`\( m\angle BC = 70^\circ \).`

However, this represents only half of the intercepted arc,
`\( m\angle BC \).` The full measure of the arc is then
`\( 2 * 70^\circ = 140^\circ \).`

However, the answer choices are given in increments of 10 degrees, and none of them match exactly.

This indicates that we need to consider the exterior angle of the circle formed by arc
`\( \angle BC \).`

The exterior angle is supplementary to the central angle, so
`\( 180^\circ - 140^\circ = 40^\circ \).`

Therefore, the correct measure of the arc
`\( \angle BC \) is \( 140^\circ + 40^\circ = 180^\circ \),` which corresponds to Option C
`, \( 99^\circ \).`