In triangle ABC, angle ABC measures 40 degrees. The circles with diameters AB and BC intersect the line that joins their centers at points D and E as shown in the figure. Find the measure of angle DBE.
|Triangle||A three-sided polygon||The sum of the three interior angles of any triangle is always equal to 180 degrees|
|Circle||A closed curve consisting of all points that are equidistant from a given point called the center||All radii of a circle are congruent (i.e., they have the same length).|
|Diameter||A line segment that passes through the center of a circle and has both endpoints on the circle||Diameter theorem - in any circle, the diameter is the longest chord.|
|Inscribed angle||An angle whose vertex is on the circle and whose sides are chords of the circle||Inscribed angle theorem - the measure of an inscribed angle in a circle is half the measure of the intercepted arc.|
|Central angle||An angle whose vertex is at the center of a circle and whose sides are radii of the circle||Central angle theorem - the measure of a central angle is equal to the measure of the arc it intercepts.|
In math class, we sit and ponder,
The angles in a triangle, a math wonder,
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o let's dive in, and unlock the mystery,
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The measure of an angle, for all to see,
We'll conquer math, with a powerful might,
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