Question

study the image.

circle o has diameter ad that intercepts the circle at a and d. inscribed angle abd also intercepts the circle at a and d.

what is the measure of ∠abd?

use the keypad to enter your answer in the box. include the correct symbol for the units of measure.

Explanation:

Step1: Recall the Thales' theorem

Thales' theorem states that if you have a triangle inscribed in a circle where one side of the triangle is the diameter of the circle, then the angle opposite that side (the inscribed angle) is a right angle (90 degrees). In this case, \(AD\) is the diameter of circle \(O\), and \(\angle ABD\) is an inscribed angle that intercepts the diameter \(AD\). So, by Thales' theorem, \(\angle ABD\) should be a right angle.

Step2: Determine the measure

Since a right angle measures \(90^\circ\), the measure of \(\angle ABD\) is \(90^\circ\).

Answer:

\(90^\circ\)