Find the value of x in the given figure chapter circle class 9 maths
Answers
Answer:
Step-by-step explanation:
- 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 .
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