Question : ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and $\angle $ADC = 118°. What is the measure of $\angle$BAC?
Option 1: 28°
Option 2: 45°
Option 3: 32°
Option 4: 30°
Correct Answer: 28°
Solution :
Given that ABCD is a cyclic quadrilateral and AB is the diameter of the circle circumscribing it, we know that $\angle$ACB = 90º.
We are also given that $\angle$ADC = 118º.
We can use the fact that the sum of opposite angles in a cyclic quadrilateral is 180º.
⇒ $\angle$ABC = 180º – $\angle$ADC=180º – 118º = 62º
In $\triangle$ABC,
⇒ $\angle$BAC + $\angle$ABC + $\angle$ACB = 180º
⇒ $\angle$BAC + 62º + 90º = 180º
⇒ $\angle$BAC = 28º
Hence, the correct answer is 28º.
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