An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
The proof discusses the relationship between arcs and inscribed angles in a circle.
The inscribed angle theorem states that an inscribed angle's measure is half its intercepted arc's measure.
The missing theorem in the proof is the inscribed angle theorem.
Therefore, the answer is inscribed angle.
Explanation
Problem Analysis The problem asks us to identify the missing theorem in a paragraph proof about the properties of a quadrilateral inscribed in a circle. The proof relates the measures of arcs and inscribed angles. The key relationship is how an inscribed angle relates to its intercepted arc.
Applying the Inscribed Angle Theorem The inscribed angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In the given proof, m an g l e A is stated to be 2 a degrees, where a ∘ is the measure of arc BC D . Similarly, m an g l e C is stated to be 2 360 − a degrees, where ( 360 − a ) ∘ is the measure of arc B A D . This directly applies the inscribed angle theorem.
Conclusion Therefore, the missing theorem is the inscribed angle theorem.
Examples
Imagine you're designing a circular window with decorative chords. The inscribed angle theorem helps you determine the angles formed by these chords and the arcs they intercept, ensuring your design is geometrically sound and visually appealing. For example, if an arc measures 80 degrees, the inscribed angle that intercepts this arc will measure half of that, which is 40 degrees. This understanding is crucial for creating balanced and aesthetically pleasing designs in architecture and art.
The number of electrons flowing through the device is approximately 2.81 × 1 0 21 . This is calculated by first finding the total charge delivered and then dividing by the charge of a single electron. The calculations show that for a current of 15.0 A over 30 seconds, this number of electrons passes through the device.
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