Solving for x and y using Intersecting Chords Theorem
To solve for the values of x and y, we can use the intersecting chords theorem, which states that the angle formed by two intersecting chords is equal to half the sum of the measures of the arcs opposite those angles.
Looking at the angles given in the image:
1. The angle opposite to the 107° arc is y°.
2. The angle opposite to the 83° arc is x°.
The angles that intercept the same arcs are supplementary, meaning that x + 107 = 180 and y + 83 = 180.
Let's solve for x and y:
For x:
x + 107 = 180
x = 180 - 107
x = 73
For y:
y + 83 = 180
y = 180 - 83
y = 97
So, the values of x and y are 73 and 97, respectively.
