Question

a tangent - tangent angle intercepts two arcs,that measure 124° and 236°. what is the measure of the tangent - tangent angle?
a. 224°
b. 180°
c. 56°
d. 112°

Explanation:

Step1: Recall the formula

The measure of a tangent - tangent angle is given by $\frac{1}{2}(m\overparen{major}-m\overparen{minor})$, where $m\overparen{major}$ is the measure of the major arc and $m\overparen{minor}$ is the measure of the minor arc.

Step2: Identify major and minor arcs

The major arc measures $236^{\circ}$ and the minor arc measures $124^{\circ}$.

Step3: Calculate the angle

Substitute the values into the formula: $\frac{1}{2}(236 - 124)=\frac{1}{2}(112)=56^{\circ}$

Answer:

C. $56^{\circ}$