Question 1 of 25A tangent-tangent angle intercepts two arcs that measure 124 and 236. What is the measure of the tangent-tangent angle?A.112B.56C.224D.180

1. Break Down the Problem

To find the measure of the tangent-tangent angle, we need to understand the relationship between the angle and the arcs it intercepts. The angle formed by two tangent lines from a point outside the circle is half the difference of the measures of the arcs intercepted by those tangents.

2. Relevant Concepts

The formula for the tangent-tangent angle $\theta$ is given by: $\theta = \frac{1}{2} \times (m_1 - m_2)$ where $m_1$ and $m_2$ are the measures of the intercepted arcs.

3. Analysis and Detail

Given the measures of the arcs:

• $m_1 = 236^\circ$
• $m_2 = 124^\circ$

Now, apply the values to the formula: $\theta = \frac{1}{2} \times (236 - 124)$

Calculating the difference: $236 - 124 = 112$

Now, substituting back into the formula: $\theta = \frac{1}{2} \times 112 = 56^\circ$

4. Verify and Summarize

The calculation shows that the tangent-tangent angle measures $56^\circ$.

Final Answer

The measure of the tangent-tangent angle is $\boxed{56}$.