Question

in the given figure angle ABC=25° then angle AOC=_____​

Answer 1

Given:

abc = 25

BAO = OCB (radii makes 90° with the tangents at the point of                                            contact)

to find:

COA

let  COA be x

SOlution:

ABC + COA + BCO + BAO = 360 (sum of all the interior angles in a quadrilateral)

25 + x + 90 + 90 = 360

x + 205 = 360

x = 360 - 205

x = 155°

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Answer 2

Given:

angle ABC=25°

To find:

The measurement of the angle AOC

Solution:

We have given the figure in AB and AC are the tangent of the circle.

And we know that the angle between the tangent and the radius of the circle is a right angle. Which is equal to 90°

And in any quadrilateral by the angle sum property, the sum of all the angles of the quadrilateral is 360°.

∠A + ∠B + ∠C + ∠O = 360°

∠O + 90° + 90° + 25° = 360°

∠O + 205° = 360°

∠O = 360° - 205°

∠O = 155°

Hence,

The measurement of the angle AOC is 155°