Applying the angles of intersecting secants theorem, the measure of angle ACB is: 16°.
<h3>What is the Angles of Intersecting Secants Theorem?</h3>
The angles of intersecting secants theorem states that the angle formed by two lines (secants or a tangent and a secant) that intersect outside a circle equals half the difference of the measure of the intercepted arcs.
Find m(XA) based on the inscribed angle theorem:
m(XA) = 2(m∠CBA)
Substitute
m(XA) = 2(42)
m(XA) = 84°
Based on the angles of intersecting secants theorem, we would have:
m∠ACB = 1/2[m(AB) - m(XA)]
Substitute
m∠ACB = 1/2[100 - 84]
m∠ACB = 16°
Therefore, applying the angles of intersecting secants theorem, the measure of angle ACB is: 16°.
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