Question

Which of the following best describes XYZ

Answer 1

Answer:

D. Inscribed angle

Step-by-step explanation:

An inscribed angle has a vertex on the circumference. For any arc, every inscribed angle is exactly half of the central angle. In other words, if the central angle is $x^{\circ}$ and the inscribed angles is $y^{\circ}$, then it is true that:

$y^{\circ}=\frac{x^{\circ}}{2}$

In this problem $y^{\circ}=36^{\circ}$, then the central angle is $x^{\circ}=2y^{\circ} \ \therefore x^{\circ}=2(36^{\circ}) \therefore x^{\circ}=72^{\circ}$

Answer 2

Answer:

Option D.

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

$m<XYZ=\frac{1}{2}(arc\ XZ)$

In this problem  

The measure of angle XYZ is an inscribed angle