Question

module 2 topic 1 assessment review

1. consider the circle on the right

a. identify a minor arc.
b. identify a major arc.
c. identify a semicircle.
d. identify 2 inscribed angles.
e. identify 2 central angles.
f. if ∠adf is 57°, what is the measure of \\(\widehat{af}\\).
determine whether it is possible to form a triangle using each set of segments with the given measurements. explain your reasoning
a. 3, 5, 7
b. 6, 10, 20

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.

Step2: Apply the theorem

Given that \(\angle ADF\) is an inscribed angle and \(\angle ADF = 57^{\circ}\). Let the central angle that subtends arc \(\widehat{AF}\) be \(\angle ACF\) (assuming \(C\) is the center). By the inscribed - angle theorem \(m\angle ADF=\frac{1}{2}m\widehat{AF}\).
If \(m\angle ADF = 57^{\circ}\), then \(m\widehat{AF}=2\times m\angle ADF\).

Answer:

\(114^{\circ}\)