Answer:
The measure of m∠KNY is;
(D) 105°
Step-by-step explanation:
From the diagram, we have;
The given angle at the circumference = The The angle the arcs makes at the center of the circle
From circle, theorem, angle subtended at the center = Twice the angle subtended at the circumference
Therefore;
Angle ∠D and angle ∠Y = 90°/2 = 45°
Angle ∠O and angle ∠K = 60°/2 = 30°
From angle summation theorem, we have;
m∠KNY + ∠K + ∠Y = 180° (The sum of the interion angles in ΔYNK
∴ m∠KNY = 180° - (∠K + ∠Y)
Plugging in the known values of ∠K and ∠Y gives;
m∠KNY = 180° - (30° + 45°) = 105°
m∠KNY = 105°.