In the following figure, find the value of x:
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Solution :
i ) In ∆ABC , <A = 40°
AB = AC
<BCA = <ABC = y [ Angles opposite to
equal angles are equal ]
<A + y + y = 180°
[ Angle sum property ]
40 + 2y = 180
=> 2y = 180 - 40
==> 2y = 140
=> y = 140/2
=> y = 70°
Now ,
In ∆ABC , BC is extended to D,
external angle at C = sum of interior
opposite angles
=> x = <A + <ABC
=> x = 40 + 70
=> x = 110°
••••
i ) In ∆ABC , <A = 40°
AB = AC
<BCA = <ABC = y [ Angles opposite to
equal angles are equal ]
<A + y + y = 180°
[ Angle sum property ]
40 + 2y = 180
=> 2y = 180 - 40
==> 2y = 140
=> y = 140/2
=> y = 70°
Now ,
In ∆ABC , BC is extended to D,
external angle at C = sum of interior
opposite angles
=> x = <A + <ABC
=> x = 40 + 70
=> x = 110°
••••
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