Answer:
The measure of arc DEF is 204° ⇒ answer C
Step-by-step explanation:
* Lets talk about some facts in the circle
- If the vertex of an angle on the circle and the two sides of the
angle are chords in the circle, then this angle is called
an inscribed angle
- Each inscribed angle subtended by the opposite arc, the arc name
is the starting point and the ending point of the angle
- The measure of any circle is 360°
# Ex: ∠CAB is inscribed angle subtended by arc CB
- There is a relation between the inscribed angle and its
subtended arc, the measure of the inscribed angle equals half
the measure of its subtended arc
* Now lets solve the problem
- ∠DEF is an inscribed angle subtended by arc DF
∴ m∠DEF = (1/2) measure of arc DF
∵ The measure of ∠DEF = 78°
∴ 78° = (1/2) measure of arc DF ⇒ multiply both sides by 2
∴ The measure of arc DF = 78° × 2 = 156°
∵ The measure of arc DF + The measure of arc DEF = The measure of
the circle
∵ The measure of the circle = 360°
∵ The measure of the arc DF = 156°
∴ 156° + measure of arc DEF = 360° ⇒ subtract 156 from both sides
∴ The measure of arc DEF = 360° - 156° = 204°
* The measure of arc DEF is 204°
