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Answer :
Final answer:
To find the measure of the arc ba, use the angles apb, apc, and bpc to set up an equation and solve for y. Then, substitute the value of y to find the measure of the arc.
Explanation:
To find the measure of the arc ba, we need to find the value of y. We have the following information:
- The angle apb is 4y + 6 degrees.
- The angle apc is 7y - 7 degrees.
- The angle bpc is 20y - 11 degrees.
We can set up an equation using the fact that the sum of the angles in a triangle is 180 degrees:
4y + 6 + 7y - 7 + 20y - 11 = 180
Simplifying the equation, we get:
31y - 12 = 180
Now, solve for y:
31y = 192
y ≈ 6.19
Now that we have the value of y, we can find the measure of the arc ba by substituting it into the expression for the angle:
arc ba = 4(6.19) + 6 = 31.76 degrees
Learn more about Angles in a Circle here:
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