Applying the angle of intersecting tangents theorem, m∠ABC = 99°
What is the Angle of Intersecting Tangents Theorem?
If two tangents intersect and form an angle outside a circle, based on the angle of intersecting tangents theorem, the angle formed equals half the positive difference of the intercepted arcs.
Given the following:
- m(AD) = (17x + 2)
- m(AC) = (7x – 10)
- m∠ABC = (4x + 15),
Apply the angle of intersecting tangents theorem:
m∠ABC = 1/2[m(AD) - m(AC)]
Substitute
4x + 15 = 1/2[(17x + 2) - (7x - 10)]
2(4x + 15) = 17x + 2 - 7x + 10
8x + 30 = 10x - 12
8x - 10x = -30 - 12
-2x = -42
x = -42/-2
x = 21
m∠ABC = (4x + 15)
Plug in the value of x
m∠ABC = 4(21) + 15 = 99°
Learn more about the angle of intersecting tangents theorem on:
https://brainly.com/question/9143293
