Question

m∠txz = 69°, find mxt.

Explanation:

Step1: Recall the tangent - secant angle formula

The measure of an angle formed by a tangent and a secant is given by \(m\angle TXZ=\frac{1}{2}(m\overset{\frown}{XT})\) (where the arc is the intercepted arc).

Step2: Solve for \(m\overset{\frown}{XT}\)

Given \(m\angle TXZ = 69^{\circ}\), we can use the formula \(m\angle TXZ=\frac{1}{2}(m\overset{\frown}{XT})\).
Multiply both sides of the equation by \(2\): \(m\overset{\frown}{XT}=2\times m\angle TXZ\).

Substitute \(m\angle TXZ = 69^{\circ}\) into the equation: \(m\overset{\frown}{XT}=2\times69^{\circ}\).

Answer:

\(138^{\circ}\)