Question

a tangent - tangent angle intercepts two arcs that measure 135° and 225°. what is the measure of the tangent - tangent angle?
a. 135°
b. 180°
c. 90°
d. 45°

Explanation:

Step1: Recall the formula

The measure of a tangent - tangent angle is given by $\frac{1}{2}(|m\overset{\frown}{AB}-m\overset{\frown}{CD}|)$, where $\overset{\frown}{AB}$ and $\overset{\frown}{CD}$ are the intercepted arcs.

Step2: Substitute the arc measures

Let $m\overset{\frown}{AB} = 225^{\circ}$ and $m\overset{\frown}{CD}=135^{\circ}$. Then the measure of the tangent - tangent angle $\theta=\frac{1}{2}(225 - 135)$.

Step3: Calculate the result

$\theta=\frac{1}{2}(90^{\circ}) = 45^{\circ}$.

Answer:

D. 45°