A circle is centered on point $B$. Points $A, C$ and $D$ lie on its circumference.
If $\angle A B C$ measures $124^{\circ}$, what does $\angle A D C$ measure?
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Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the relationship between the central angle and the inscribed angle that intercepts the same arc. ‖ ‖ step 2 ⋮ Recognize that the central angle is twice the inscribed angle. ‖ ‖ step 3 ⋮ Calculate the measure of the central angle $BCD$ using the given inscribed angle $ABC$ which is $124^\circ$. ‖ ‖ step 4 ⋮ Since $BCD$ is a central angle, $BCD = 2 imes ABC = 2 imes 124^\circ = 248^\circ$. ‖ ‖ step 5 ⋮ Determine the measure of the arc $ACD$ that the angle $BCD$ intercepts, which is also $248^\circ$. ‖ ‖ step 6 ⋮ Recognize that the angle $ADC$ is an inscribed angle that intercepts the same arc $ACD$. ‖ ‖ step 7 ⋮ Calculate the measure of the inscribed angle $ADC$ which is half of the central angle, so $ADC = \frac{1}{2} imes BCD = \frac{1}{2} imes 248^\circ = 124^\circ$. ‖ ∻Answer∻ ⚹ The measure of angle $ADC$ is $124^\circ$. ⚹ ∻Key Concept∻ ⚹Central and Inscribed Angles⚹ ∻Explanation∻ ⚹The central angle is twice the measure of an inscribed angle that intercepts the same arc. The inscribed angle $ADC$ and the central angle $BCD$ intercept the same arc $ACD$, so the measure of $ADC$ is half of $BCD$.⚹◊What is the measure of angle ADC in degrees?⍭ Generate me a similar question◊

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