Question

fall 2025 geometry b wwva
inscribed angles
line segment xy is tangent to circle z at point u
if the measure of arc uv is 84°, what is the measure of ∠yuv?
options: 84°, 168°, 42°, 96°

Explanation:

Step1: Recall tangent-chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of its intercepted arc.

Step2: Apply the theorem to ∠YUV

Intercepted arc of ∠YUV is $\widehat{UV} = 84^\circ$. So $\angle YUV = \frac{1}{2} \times 84^\circ = 42^\circ$.

Answer:

42°