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oksano4ka [1.4K]
3 years ago
7

5. The measure of an intercepted arc is 86, and the measure of the inscribed angle creating the intercepted arc is 3x +

Mathematics
1 answer:
Nonamiya [84]3 years ago
4 0

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.

\textrm{Angle Inscribed in arc}=\dfrac{1}{2}\textrm{Center Angle}

Substituting the values we get

3x+4=\dfrac{1}{2}86=43\\\\3x=39\\\\x=\dfrac{39}{3}=13\\\\x=13

Therefore the value of x is 13.

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