ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 118°. What is the measure of ∠BAC?
Answer & explanation
Correct answer: option 1
In a cyclic quadrilateral, the sum of each pair of opposite angles is 180 degrees.
= \(\angle\)ADC + \(\angle\)ABC = 180
= 118 + \(\angle\)ABC = 180
= \(\angle\)ABC = \({62}^\circ\)
= \(\angle\)ACB = \({62}^\circ\) (The angle formed by the diameter of the circle at the circumference of the circle always 90.)
In \(\Delta \)ABC,
= \(\angle\)BAC + \(\angle\)ACB + \(\angle\)ABC = 180
= \(\angle\)BAC + 90 + 62 = 180
= \(\angle\)BAC = 28
Therefore, \(\angle\)BAC is \({28}^\circ\).