Question

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Answer 1

Answer:

To solve this question, we need to know two important properties of circle.

1. The angle subtended by an arc of a circle at its centre is twice of the angle it subtends anywhere on the circle's circumference.

2. Circumcenter is the center of a circle which touches all the three vertices of the triangle while circumscribed.

Now according to the question,

⇒ Angle B = 72° and Angle C = 68°.

Hence by Angle Sum property we get Angle A to be:

⇒ A + 72 + 68 = 180°

⇒ A + 140° = 180°

⇒ A = 180° - 140°

⇒ A = 40°

Hence Angle A is 40°.

Now, according to the diagram (Attached), we see Angle A and Angle O are the angles subtended by the arc BC. Hence according to the theorem we get:

⇒ Angle O = 2 × Angle A

⇒ Angle O = 2 × 40°

⇒ Angle O = 80°

Hence Angle OBC is 80°.

Answer 2

Given

• ∠ ABC = 72°
• ∠ ACB = 68°

We Find

• Measures of ∠OBC

We used

We used Angle sum property to find ∠A

According to the question

By Angle sum property, we get value of A :-

A + 72° + 68° = 180°

= A + 140° = 180°

= A = 180° - 140°

= A = 40°

So, Angle A = 40°

Then according to Diagram, We used a Formula to find ∠OBC. so, Theorm is given

= Angle O = 2 × Angle A

= Angle O = 2 × 40°

= Angle O = 80°

So, Angle ∠OBC is 80° .

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