Question

Find the value of x. A) 9 b) 10 c) 11 d) 12.

Answer 1

Applying the inscribed angle theorem, the value of x is: A. 9

The Inscribed Angle Theorem

Based on the inscribed angle theorem, the measure of intercepted arc is twice the size of the inscribed angle in a circle.

Thus, considering the image attached below, applying the the inscribed angle theorem, we will have:

DF = 2(m∠DEF)

• Substitute

70 = 2(8 + 3x)

70 = 16 + 6x

70 - 16 = 6x

54 = 6x

• Divide both sides by 6

9 = x

x = 9

Therefore, applying the inscribed angle theorem, the value of x is: A. 9

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