Urgent and pls explain thoroughly. O is the centre of the circle. OA, OB and OC are radii. Angle AOB = 72°. Work out
a) angle OAB b) angle OCB c) angle ABC

<ABC=90° <OCB=36° <OAB=54°

Step-by-step explanation:

<ABC=90°

<ocb= half of aob

<oab + <abc+<ocb=180°(triangle abc)

a) ∠OAB = 54°

b) ∠OCB = 36°

c) ∠ABC = 90°

Step-by-step explanation:

a)

If O is the center of the circle, then OA and OB are both the radius.  Therefore, OA = OB

This means that ΔAOB is an isosceles triangle, as is has two sides of equal length (OA and OB).  

The angle between the equal sides (∠AOB) is called the vertex angle.  The side opposite the vertex angle (AB) is called the base and base angles are equal. Therefore, ∠OAB = ∠OBA

Given:

⇒ ∠OAB + ∠OBA + ∠AOB = 180

⇒ ∠OAB + ∠OBA + 72 = 180

⇒ ∠OAB + ∠OBA = 108

⇒ ∠OAB = 108 ÷ 2 = 54°

b)

Again, we can see that OB and OC are both the radius, so OB = OC.  This means that ΔBOC is also an isosceles triangle, with ∠BOC as the vertex and BC as the base.

Calculate ∠BOC:

Given:

⇒ ∠AOB + ∠BOC = 180

⇒  72 + ∠BOC = 180

⇒ ∠BOC = 108°

Calculate ∠OCB:

Given:

⇒ ∠OBC + ∠OCB + ∠BOC  = 180

⇒ ∠OBC + ∠OCB + 108  = 180

⇒ ∠OBC + ∠OCB  = 72

⇒ ∠OCB  = 72 ÷ 2 = 36°

c)

Thales's theorem is a special case of the inscribed angle theorem and states that:

Given that AC is the diameter of this circle, and points A, B and C are on the circle, then ∠ABC = 90°

your answer is b ^w^ hope i

step-by-step explanation: