Question

What is the measure of AR in O below ? PLEASE HELP

Answer 1

arcs get their angle measurement from the central angle they're in.

in this case, the central ∡AOR is 142°, it just so happen that the ∡AOR is the central angle of arcAR.

Answer 2

Option B 142 degrees

Explanation:

Given is a circle with centre O

A and R are points on the circumference

AOR is given as 142 degrees

AOR angle is nothing but the arc (minor) AR subtends at the centre.

Hence measure of AR = angle the minor arc AR subtends at the centre

= 142 degrees

Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). The central angle is also known as the arc's angular distance. The size of a central angle Θ is 0° < Θ < 360° or 0 < Θ < 2π (radians).