Question

no additional details were added for this assignment.
examine circle q, which has a diameter re that intercepts the circle at r and e.
inscribed angle rde also intercepts the circle at r and e.
what is the measure of ∠rde?
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. In formula terms, if \( RE \) is the diameter of circle \( Q \) and \( \angle RDE \) is an inscribed angle subtended by \( RE \), then \( \angle RDE = 90^\circ \).

Step2: Apply the theorem to the given problem

In circle \( Q \), \( RE \) is the diameter, so the arc \( RE \) is a semicircle, which measures \( 180^\circ \). The inscribed angle \( \angle RDE \) subtends arc \( RE \). The measure of an inscribed angle is half the measure of its subtended arc. So, \( \angle RDE=\frac{1}{2}\times\text{measure of arc } RE \). Since arc \( RE = 180^\circ \), then \( \angle RDE=\frac{1}{2}\times180^\circ = 90^\circ \).

Answer:

\( 90^\circ \)