Question

in figure O is the centre of circle And angle acb=40. Find angle oab

Answer 1

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Answer 2

Given:

• ∠ACB = 40°

To Find:

• The measure of the angle OAB

Solution:

• In the given figure, the angle subtended by an arc from the center is formed.
• So, the angle subtended is twice the remaining part of the circle.
• Therefore, ∠AOB = 2*∠ACB
• ∠AOB = 2*40°
• ∠AOB = 80°
• If we observe the digram, AO and BO are the radii of the triangle AOB.
• Therefore, ∠OAB = ∠OBA (since angles opposite to equal sides are equal)
• We know that the sum of all the angles of a triangle should be 180°
• So we have from ΔAOB,
• ∠OAB+∠OBA+∠AOB = 180°
• Let 'x' = ∠OAB = ∠OBA
• x+x+80°=180°
• 2x = 180°-80°
• 2x = 100°
• x = 100/2 = 50°
• ∴∠OAB = 50°

∴ The measure of the angle OAB = 50°.