Question

what is the measure of \\( \angle boc \\) in the figure below?
a
10°
b
20°
c
30°
d
60°

Explanation:

Step1: Recall the property of a straight - line angle

A straight - line angle measures \(180^{\circ}\). In the figure, \(\angle AOC = 180^{\circ}\) (since \(A\), \(O\), and \(C\) are collinear), and \(\angle AOC=\angle AOB+\angle BOC\).

Step2: Substitute the known values

We know that \(\angle AOB = 150^{\circ}\) and \(\angle AOC = 180^{\circ}\). Using the equation \(\angle BOC=\angle AOC-\angle AOB\).
Substitute the values: \(\angle BOC=180^{\circ}- 150^{\circ}\)

Step3: Calculate the value of \(\angle BOC\)

\(\angle BOC = 30^{\circ}\)

Answer:

C. \(30^{\circ}\)