Questions: Find the value of x. 16x-22

Find the value of x. 16x-22
Transcript text: Find the value of $x$. $16 x-22$
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Solution

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Solution Steps

Step 1: Establish the relationship between the inscribed angle and the intercepted arc

The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, the measure of angle QRP is half the measure of arc QP.

Step 2: Set up an equation

Since angle QRP intercepts arc QP, we can write the equation: m∠QRP = (1/2) * m(arc QP). We are given that m∠QRP = x and m(arc QP) = (16x - 22)°. So, x = (1/2)(16x - 22)

Step 3: Solve for x

Multiplying both sides by 2, we get 2x = 16x - 22. Subtracting 2x from both sides gives 0 = 14x - 22. Adding 22 to both sides gives 22 = 14x. Finally, dividing both sides by 14 gives x = 22/14 = 11/7.

Final Answer:

The value of x is 11/7.

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