Question

Use the Above Figure to Answer the Question. What's the angle between the tangents at T in the Figure?

Answer 1

Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

∠AOT=60°

Consider Δ ATO,

As we know that the radius always forms right angle at the tangent, as the radius is the shortest distance to it .

So,  ∠OAT=90°

As we know that "Sum of interior angles of the triangles is supplementary":

$\angle A+\angle ATO+\angle AOT=180\textdegree\\\\90\textdegree+60\textdegree+\angle ATO=180\textdegree\\\\150\textdegree+\angle ATO=180\textdegree\\\\\angle ATO=180\textdegree-150\textdegree\\\\\angle ATO=30\textdegree$

so, the angle between the tangent is given by

$2\times 30\textdegree=60\textdegree$

Hence, Option 'C' is correct.

Answer 2

C 60 degrees
tangents hit circles at 90° so that means A and B are 90° O is divided in half so O is 60+ 60 to find T you need to subtract the sum of the numbers from 360 (quadrilateral degrees) 360-300=
A 90°
B 90°
O 120°
T? =60°

another way to find the answer is by using angle AOT a triangle is 180° so you are going to use that number to subtract from. Again tangents are 90° so you are going to add 90 +60 and subtract that answer from 180 to find ATO 180= 90+60+x 180=150+x. 180-150 =30.. since T is double that since it is split in half making the full total degree of T 60°