ABCD is a cyclic quadrilateral in which $\mathrm{BC}=\mathrm{CD}$ and EF is a tangent at A . $\angle \mathrm{CBD}=43^{\circ}$ and $\angle \mathrm{ADB}=62^{\circ}$. Find: $\angle \mathrm{ADC}$
Explanation
Since ABCD is a cyclic quadrilateral, the sum of the opposite angles is 180 degrees. Therefore, angle ADC + angle ABC = 180 degrees. We are given that angle CBD = 43 degrees and angle ADB = 62 degrees. Since EF is a tangent at A, angle ADB = angle ABD = 62 degrees. Therefore, angle ABC = 180 - 62 - 62 = 56 degrees. Now, we can find angle ADC by subtracting angle ABC from 180 degrees: angle ADC = 180 - 56 = 124 degrees.
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