A) find the length of each radius (radius of circle m and radius of circle n).

b) what does "point of tangency" mean? and identify the point of tangency.

c) write the equation of the tangent line at this point.

A) From the graph,
.. radius of M is 1
.. radius of N is 3

B) The "point of tangency" is the one point where the circles and tangent line meet. That point is (2, 1).

C) The horizontal tangent line has equation
.. y = 1

x=37.5° and angle ABC is 52.5°Step-by-step explanation:

We know that angle CBD is a right angle.

We also know that angle ABE is 180°.

Our unknown angle values are angle DBE and angle CBA.

angle CBD minus angle ABE will be 90°.

angle ABC plus angle DBE must equal 90°.

Solving for x:

(x+15)+(x)=90°

(x+15-15)+(x)=90°-15

(x)+(x)=75°

2x=75°

2x/2=75°/2

x=37.5°

Checking the work:

ABC=37.5°+15=52.5°

CBD=90°

DBE=37.5°

In conclusion, ABC plus CBD plus DBE equals 180°

Hope this helped!