Question

Suppose that m∠MKN = 55°. What is m∠MCN? !please no absurd answers!

Answer 1

Taking into account that in the point of contact, the tangent to a circle is perpendicular to the radius, we have angles KMC = angle KNC = 90⁰.

In a 4-sides polygon (KMCN), the sum of all angles is 360⁰:

55+90+MCN+90=360

MCN=180-55=125⁰

Answer: MCN=125⁰

Answer 2

Answer:

angle M and N are right angles

we can draw a line joining M and N  

so we’d have a triangle MNC AND KMN

both MNC AND KMN BECOME ISOSCELES TRIANGLES

so since we have 55 degrees for angle MKN. We have to find the other 2

180-55=125

now divide by 2 to get 62.5 for each of the remaining sides of triangle KMN

now to find the sides of triangle MNC

90-62.5= 27.5

27.5*2= 55

180-55=125=angle C

(sorry, it’s complex)