Question

Using the given figure where KMarrowright and KNarrowright are tangent to the circle at M and N, respectively. What can you say about the following?

What angles are right angles?

The right angles are ∠ ? and ∠ ? .

Suppose that m∠MKN = 50°. What is m∠MCN?

m∠MCN is °.

Answer 1

1) ∠CMK and ∠CNK

2) 140 degrees

Explanation:

The angle between the tangent of a circle the radius of the circle is always 90 degrees or a Right Angle. Since KM and KN are tangents to the given circle and MC and NC are the radii of the circle, so the ∠ CMK and the ∠ CNK would be the right angles.

The figure CMKN would be a quadrilateral. Sum of angles of a quadrilateral is always 360 degrees.

∠MNK is given to be 50 degrees.

Sum of angles must be 360, so we can write:

∠CMK + ∠MKN + ∠CNK + ∠MCN = 360

90 + 50 + 90 + ∠MCN = 360

∠MCN = 140 degrees.

Thus, the measure of ∠MCN is 140 degrees.