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Can someone please explain step by step so I can understand

Can someone please explain step by step so I can understand-example-1
User Madper
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Answer:


\sf\\\textsf{An exterior angle of a triangle is equal to the sum of the opposite interior angles.}\\\therefore\ x^o+81^o=123^o\\\textsf{or, }x^o=42^o

See how this theorem works:


\sf\\\textsf{In the triangle given below, we need to show that }\angle a+\angle b=\angle d.\\\textsf{Now we know that:}\\\angle a+\angle b+\angle c=180^o\ \ \ [\textsf{Sum of interior angles of a triangle is }180^o.]\\\textsf{or, }\angle a+\angle b=180^o-\angle c...............(1)


\sf\\\textsf{Also, }\angle c\textsf{ and }\angle d\textsf{ are two angles on a straight line. Therefore they add up to }180^o.\\\angle c+\angle d=180^o\\\textsf{or, }\angle d=180^o-\angle c\\\\\textsf{From equation(1),}\\\angle d=\angle a+\angle b


\textsf{Hence, exterior angle of a triangle is equal to sum of two opposite interior angles.}

Can someone please explain step by step so I can understand-example-1
User Zeyad Gasser
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