I don’t understand what this question is asking for

Mathematics

1 answer:

Elden [556K]2 years ago

7 0

Answer:

(d) m∠AEB = m∠ADB

Step-by-step explanation:

The question is asking you to compare the measures of two inscribed angles. Each of the inscribed angles intercepts the circle at points A and B, which are the endpoints of a diameter.

<h3>applicable relations</h3>

Several relations are involved here.

The measures of the arcs of a circle total 360°
A diameter cuts a circle into two congruent semicircles
The measure of an inscribed angle is half the measure of the arc it intercepts

<h3>application</h3>

In the attached diagram, we have shown inscribed angle ADB in blue. The semicircular arc it intercepts is also shown in blue. A semicircle is half a circle, so its arc measure is half of 360°. Arc AEB is 180°. That means inscribed angle ADB measures half of 180°, or 90°. (It is shown as a right angle on the diagram.)

If Brenda draws angle AEB, it would look like the angle shown in red on the diagram. It intercepts semicircular arc ADB, which has a measure of 180°. So, angle AEB will be half that, or 180°/2 = 90°.

The question is asking you to recognize that ∠ADB = 90° and ∠AEB = 90° have the same measure.

m∠AEB = m∠ADB

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<em>Additional comment</em>

Every angle inscribed in a semicircle is a right angle. The center of the semicircle is the midpoint of the hypotenuse of the right triangle. This fact turns out to be useful in many ways.