Math, asked by poorvitha4262, 1 year ago

Find the value of x in the given figure chapter circle class 9 maths

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Answered by utimohityadav
8

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Answered by RvChaudharY50
2
  • The value of x in the given figure is equal to 50° .

Complete Question :- Find the value of x in the given figure in which O is the centre of the circle ? ( class 9 maths )

Concept used :-

  • Angle at centre is double of angle at circumference .
  • Angle opposite to equal sides of a triangle are equal in measure .
  • Sum of all three angles of a triangle is equal to 180° .

Solution :-

from image we can see that,

→ ∠BAC = 40° { Angle at circumference of the circle }

So,

→ ∠BOC = 2•∠BAC { Angle at centre is double of angle at circumference }

→ ∠BOC = 2 × 40°

→ ∠BOC = 80° -------- Equation (1)

now in ∆BOC we have,

→ OB = OC { Radii of the circle }

So,

→ ∠OBC = ∠OCB = x { Angle opposite to equal sides of a triangle are equal in measure } ------ Equation (2)

then,

→ ∠OBC + ∠OCB + ∠BOC = 180° { Angle sum property of a triangle }

putting values from Equation (1) and Equation (2) we get,

→ x + x + 80° = 180°

→ 2x + 80° = 180°

→ 2x = 180° - 80°

→ 2x = 100°

dividing both sides by 2,

→ x = 50° (Ans.)

Hence, the value of x is equal to 50° .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

https://brainly.in/question/32333207

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