Question

Can someone please explain step by step so I can understand

Answer 1

`\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.}`