Question

Given: BT diameter of Circle P.

Angle BTP is 20 degrees (m3 = 20°).
Find: The measure of angle A (mA).

Options:
A) 160
B) 50
C) 140

Answer 1

To find the measure of angle A in circle P, we can use the properties of inscribed angles and triangles.

Step-by-step explanation:

To find the measure of angle A, we need to consider the properties of circles and angles. In a circle, the measure of an inscribed angle is half the measure of the intercepted arc. Given that angle BTP is 20 degrees, we can conclude that the intercepted arc BT has a measure of 40 degrees. Since angle PBT is a central angle, it is equal to the measure of the intercepted arc BT. Therefore, angle PBT is 40 degrees.

Since the sum of the angles in a triangle is 180 degrees, we can find angle A using the equation 180 = 20 + 40 + mA. Simplifying the equation gives us mA = 120 degrees. Therefore, the measure of angle A is 120 degrees.