#### 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

Anonymous

0

(a) Work out the size of angle WOZ.

(b) Work out the size of angle WXY

Krishna

0

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