The value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
<h3>What is a circle?</h3>
It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that:
A circle is shown in the picture.
PTR is the tangent of a circle.
AT=PT
Angle APT=20°
Let O is the center of the circle:
Angle BOT = 2 Angle PAT = 40 degrees
BO = TO = r
Angle BOT = Angle TBO = (1/2)(180 - 40) = 70 degrees
RTP is the tangent
OT ⊥ PTR
Angle OTA = 90 - Angle ATR = 50 degrees
Angle ABT = 180 - Angle PAT - Angle BTA
= 180 - 20 - (170 + 50)
= 40 degrees
Thus, the value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
Learn more about circle here:
brainly.com/question/11833983
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