High School

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Observe the circle [p] below. A circle is centered around point P. Points A, B, and C all lie on this circle in a clockwise direction. Line segments AP, BP, and CP are radii of the circle. The angle ∠APB is [tex](4y + 6)^\circ[/tex]. The angle ∠APC is [tex](7y - 7)^\circ[/tex]. The angle ∠BPC is [tex](20y - 11)^\circ[/tex].

What is the measure of arc [tex]\overset{\large\frown}{BA}[/tex] in degrees?

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:

  1. The angle apb is 4y + 6 degrees.
  2. The angle apc is 7y - 7 degrees.
  3. 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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Rewritten by : Jeany