6. Applying the inscribed angle theorem, x = 33
7. m<ABP = 90°.
m<APB = 48°
The tangent theorem states that the tangent of a circle is perpendicular to the radius of that circle and therefore forms a right angle at the point of tangency.
An inscribed angle has a measure that is half the measure of the intercepted arc, according to the inscribed angle theorem.
Therefore:
Question 6:
Based on the inscribed angle theorem,
Measure of arc AB = 2(x + 3) = 2x + 6
108 + 2x + 6 = 180 [semicircle]
Solve for x
114 + 2x = 180
2x = 180 - 114
2x = 66
x = 33
Question 7:
Given that line PB is tangent to circle A, therefore, based on the tangent theorem, the measure of angle ABP = 90°.
m<APB = 180 - 90 - 42
m<APB = 48°
Learn more about the tangent theorem on:
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