Question

Can someone work this one out with me please

Answer 1

46°

Explanation:

Since the side mn is tangent, the angle in M is a right angle. The sum of internal angles needs to add to 180°, so subtacting you're left with 46°

Answer 2

Hi there!

Since MN is tangent to Circle K, we know that MK and MN are PERPENDICULAR.

Therefore, m∠M = 90°.

Since we now know two angles in the right triangle, we can solve for m∠K knowing that angles in a triangle sum up to 180°.

180° = ∠M + ∠N + ∠K

180° = 90° + 44° + ∠K

Combine like terms:
180° = 134° + ∠K

Subtract:
180° - 134° = ∠K

∠K = 46°