Question

If a side of a triangle is produced, prove that the exterior angle so formed is equal to the sum of the two interior opposite angle

Answer 1

Answer:

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refer the reference diagram uploaded above for better understanding

Step-by-step explanation:

TO PROVE=

angle abc+angle+angle bac=angle acd

so let the required triangle be triangle abc

and extend bc upto d such that b-c-d

so now here

angle cab and angle acd form a pair of linear angle

thus angle acb+angle acd=180 (1)

also applying angle sum property on triangle abc

we get

angle abc+angle bca+angle+angle bac=180 (2)

so equating both equations

we get

angle abc+angle bca+angle+angle bac=angle acb+angle acd

so angle acb gets eliminated on both sides

so thus we get

angle abc+angle+angle bac=angle acd

hence proved