In the figure, a circle is centered at C with BE←→ and DE←→ drawn tangent to the circle B and D, respectively.
Calculate the m∠BAD .
A. m∠BAD=37.5°
B. m∠BAD=52.5°
C. m∠BAD=75°
D. m∠BAD=150°
Since BE and DE are tangents to the circle at points B and D, they are perpendicular to the radii drawn from the center of the circle to those points. Therefore, ∠ABC is a right angle, and, since AD is a tangent to the circle, ∠BAD is the exterior angle to triangle ABC.
Since the sum of angles in a triangle is 180°, we can calculate m∠ABC: 180 - 90 = 90°.
Therefore, m∠BAD = 180 - m∠ABC = 180 - 90 = 90°.
So, the correct answer is not among the options provided.