Question

AB is tangent to ⊙C at point B and AD is tangent to ⊙C at point D.

Circle C is shown. Line segments C B and C D are radii. Line segments B A and D A are tangents to circle C. Angle B C D is 124 degrees.

What is m∠A?
34°
62°
56°
124°

Answer 1

Answer: c

Explanation:

Answer 2

`{\qquad\qquad\huge\underline{{\sf Answer}}}`

As you can see in the quadrilateral ABCD, the two angles measure 90° (as they are tangents to circle c) and one of them is given 124°

we need to find the Angle BAD : let it be x ~

By angle sum property of Quadrilaterals,

`\qquad \sf  \dashrightarrow \: 90 + 90 + 124 + x = 360`

`\qquad \sf  \dashrightarrow \: x+30 4 = 360`

`\qquad \sf  \dashrightarrow \: x = 360 - 304`

`\qquad \sf  \dashrightarrow \: x = 56 \degree`

Hence, Angle m A = 56°