Question

best answer will be marked as the brainliest answer so the question is that in the given figure, if chords AB and CD of the circle intersect at each other at 90 degree angles , then find the sum of angles x and y !​

Answer 1

Diagram :-

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Solution :-

Here ,

∠CAO = ∠ODB

[$\boldsymbol\because$ Angles are on same line segment ]

Assuming as equation 1

Now , using angle sum property

⇒ ∠ODB + ∠OBD + ∠BOD = 180°

⇒ ∠CAO + y + 90° = 180°

⇒ x + y + 90° = 180°

⇒ x + y = 180° - 90°

⇒ x + y = 90°

Hence , sum of angles ( x + y ) = 90°

More information :-

Properties of triangles,

◉ Angle sum property :-

• Sum of all angles in a triangle is equal to 180°

◉ Exterior angle sum property :-

• Sum of all exterior angles of a traingle is always equal to 360°

◉ Exterior angle property :-

• Exterior angle equal to sum of two interior opposite angles .

◉ Isosceles triangle property :-

• Equal sides opposite angles are always equal .

Answer 2

Answer:

✳️ Given ✳️

$\mapsto$ If chords AB and CD of the circle intersect each other at 90° .

✳️ To Find ✳️

$\mapsto$ What is the sum of angle x and y.

✳️ Solution ✳️

$\leadsto$ $\angle$ACD = $\angle$ABD [ Angle in the same segment are equal ]

$\implies$ $\angle$ACD = y

➕ Consider the ∆ACM in which,

$\implies$ $\angle$ACM + x + 90° = 180°

$\implies$ y + x + 90° = 180°

$\implies$ x + y = 180° - 90°

$\dashrightarrow$ x + y = 90°

$\therefore$ The sum of angle (x + y) = 90°.

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