The size of the angles ∠AOB is 96° and ∠APB is 84°.
What is a circle?
A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.
For the given situation,
The diagram shows the circle and angle measure.
Let C be a point on the circle with O as center and
PA and PB be the tangent to the circle.
By circle theorem we know that
[tex]\angle AOB = 2 \angle ACB[/tex]
⇒ [tex]\angle AOB = 2 (48)[/tex]
⇒ [tex]\angle AOB = 96[/tex]
The sides AOBP forms the quadrilateral. So, the sum of opposite angles is 180°,
[tex]\angle AOB+ \angle APB = 180\\[/tex]
⇒ [tex]\angle APB=180-\angle AOB[/tex]
⇒ [tex]\angle APB=180-96[/tex]
⇒ [tex]\angle APB=84[/tex]
Hence we can conclude that the size of the angles ∠AOB is 96° and ∠APB is 84°.
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