9514 1404 393
Answer:
(2) 72°
Step-by-step explanation:
In this geometry, the angle at the tangent is half the measure of the intercepted arc.
∠CBD = (arc BD)/2 = 144°/2
∠CBD = 72°
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<em>Additional comment</em>
Consider a point X anywhere on long arc BD. The inscribed angle at X will have half the measure of short arc BD, so will be 144°/2 = 72°. This is true regardless of the position of X on long arc BD. Now, consider that X might be arbitrarily close to point B. The angle at X is still 72°.
As X approaches B, the chord XB approaches a tangent to the circle at B. Effectively, this tangent geometry is a limiting case of inscribed angle geometry.
