Question

question 16 of 25
a tangent - tangent angle intercepts two arcs that measure 135° and 225°. what is the measure of the tangent - tangent angle?
a. 45°
b. 90°
c. 180°
d. 135°

Explanation:

Step1: Recall tangent-tangent angle formula

The measure of a tangent-tangent angle is half the difference of the measures of its intercepted arcs. Let the larger arc be $L = 225^\circ$ and the smaller arc be $S = 135^\circ$. The formula is $\text{Angle} = \frac{1}{2}(L - S)$.

Step2: Substitute values into the formula

$\text{Angle} = \frac{1}{2}(225^\circ - 135^\circ)$

Step3: Calculate the difference first

$225^\circ - 135^\circ = 90^\circ$

Step4: Compute the final angle

$\text{Angle} = \frac{1}{2} \times 90^\circ = 45^\circ$

Answer:

A. $45^\circ$