W, X and Y are points on the circumference of a circle with centre O, ZYO is a straight line. ZW is a tangent to the circle. Angle WZO = 28

(a) Work out the size of angle WOZ.
(b) Work out the size of angle WXY
(a) Work out the size of angle WOZ.
(b) Work out the size of angle WXY
Step 1: Observe the given figure and note down the given information
Step 2: Calculate the unknown angles ( ∠OWZ) by using the hints in the question.
NOTE: According to the Perpendicular Tangent Theorem, tangent lines
are always perpendicular to a circle's radius at the point of intersection.
Tangent of the circle is always perpendicular to radius
EXAMPLE: From the figure \angle OWZ=90
Step 3: Calculate the Central angle ( \angle WOZ) by using the properties triangle
NOTE: The sum of the angles in any triangle is 180 degrees.
EXAMPLE: From the figure OWZ is a triangle.
Sum of angles in triangle = 180
\angle OWZ+\angle WOZ+\angle WZO=180
\left(\angle WOZ=180-(\angle OWZ+\angle WZO\right)
\angle WOZ=180-(90+28)
\angle WOZ=180-118
\angle WOZ=62
Step 4: Calculate the inscribed angle (∠WXY)
NOTE: The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points.
EXAMPLE: Central angle = 62
Inscribed\ angle(\angle WXY)=\frac{\text{Central angle}}{2}
Inscribed angle ∠WXY = \frac{62}{2} = 31