Answer:
Th correct option is D. 13
Therefore the value of x is 13.
Step-by-step explanation:
Given:
measure of an intercepted arc = 86°
Center Angle = 86°
measure of the inscribed angle creating the intercepted arc= (3x+4)°
Angle Inscribed in arc = (3x+4)°
To Find:
value of x = ?
Solution:
Inscribed Angle Theorem:
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
[tex]\textrm{Angle Inscribed in arc}=\dfrac{1}{2}\textrm{Center Angle}[/tex]
Substituting the values we get
[tex]3x+4=\dfrac{1}{2}86=43\\\\3x=39\\\\x=\dfrac{39}{3}=13\\\\x=13[/tex]
Therefore the value of x is 13.
