In this figure, O is the centre of the circle. Find the size of each lettered angle:
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Solution ;
i ) In ∆ABD ,
<A + <B + <D = 180°
[ Angle sum property ]
=> 90° + x + 32° = 180°
{ Since ,<A = 90° [ Angle in semicircle ]}
=> 122° + x = 180°
=> x = 180° - 122°
=> x = 58°
ii ) Similarly ,
In ∆BCD ,
<B + <C + <D = 180°
=> 50° + 90° + y = 180°
=> 140° + y = 180°
=> y = 180° - 140°
=> y = 40°
••••
i ) In ∆ABD ,
<A + <B + <D = 180°
[ Angle sum property ]
=> 90° + x + 32° = 180°
{ Since ,<A = 90° [ Angle in semicircle ]}
=> 122° + x = 180°
=> x = 180° - 122°
=> x = 58°
ii ) Similarly ,
In ∆BCD ,
<B + <C + <D = 180°
=> 50° + 90° + y = 180°
=> 140° + y = 180°
=> y = 180° - 140°
=> y = 40°
••••
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