The measure of an inscribed angle is one-half the measure of the central angle.
An inscribed angle in geometry is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle formed by two given points on a circle at a given point on the circle.
The measure of an inscribed angle is one-half the measure of the central angle. The measure of a circumscribed angle is 180 degrees minus the measure of the central angle.
Given: P lies outside
m ∠ABC = m ∠DBC – m ∠DBA ( Addition Postulate, Subtraction Property of Equality)
m ∠DBC = m 1/2(arc DC)
m ∠DBA = m 1/2(arc DA) (The measure of an inscribed ∠ whose side diameter is half the measure of the intercepted arc (Case 1)).
m ∠ABC = m 1/2 (arc DC) – m 1/2(arc DA) (Substitution)
m ∠ABC = 1/2 [m(arc DC) – m(arc DA)] (Factor)
m(arc DA) + m(arc AC) = m(arc DC) (Arc Addition Postulate)
m(arc AC) = m(arc DC) – m(arc DA) (Subtraction Property of Equality)
m ∠ABC = m 1/2 (arc AC) (Substitution)
To learn more about inscribed angle refer to:
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