Question

In figure, if ∠ATO = 40°, then find ∠AOB.

Answer 1

Answer:

<AOB = 100°

Step-by-step explanation:

Given <ATO = 40°

Proof :

i) In ΔOAT , ΔOBT

OA = OB \* radii of a same circle\*

<OAT = <OBT = 90°

\* Angle between tangent and radius

through the point of contact *\

OT =OT \*common hypotenuse *\

∴ΔOAT ≅ ΔOBT \* RHS congruence rule *\

<ATO = < OTB /* C.P.C .T*/

∴<ATO +<OTB = 2<ATO

= 2×40° [ GIVEN ]

= 80°

ii) In OATB quadrilateral,

<AOB + <OBT + <BTA + <TAO = 360°

/* Angle sum property */

<AOB + 90° + 80° + 90° = 360°

⇒ <AOB = 360° - 260°

= 100°

Answer 2

Step-by-step explanation:

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