Question

Given: DR tangent to Circle O.

Ir DB=140, then A=

A)70
B)110
C)140
D)80

The quiz says 140 is wrong, but I don’t know if that’s a problem on the teacher’s end or not, because everyone here says it’s 140

Answer 1

I believe the answer is 110.

Answer 2

110°

Explanation:

In this problem we need to use the Inscribed Angle theorem, which states that an inscribed angle is one-half its subtended arc.

`\angle C=(1)/(2)arc(DB)=70\°`

Then, we use the theorem about a cyclic quadrilateral, which is an inscribed quadrilateral: "the opposite angles in a cyclic quadrilateral are supplementary".

`\angle C + \angle A = 180\°\\\angle A = 180\° - \angle C\\\angle A = 180\° - 70\° \\\angle A = 110\°`

Therefore, the answer is 110°