Question 769301


Triangle ABC has an exterior angle, < {{{DAB}}}, and two remote interior angles, < {{{B}}} and < {{{C}}}. 

by definition, < {{{DAB}}}=< {{{B}}}+ < {{{C}}} 

If m < {{{DAB= 11x+13}}}, m < {{{B= 7x-7}}} and m < {{{C= 9x}}}, then

{{{11x+13=7x-7+9x}}}

solve {{{x}}} 

{{{11x+13=16x-7}}}

{{{7+13=16x-11x}}}

{{{20=5x}}}

{{{x=4}}}

so, m < {{{DAB= 11x+13}}} => m < {{{DAB= 11*4+13}}} => m < {{{DAB= 57}}}

m < {{{B= 7x-7}}} => m < {{{B= 7*4-7}}} => m < {{{B= 21}}}

m < {{{C= 9x}}} => m < {{{C= 9*4}}} => m < {{{C= 36}}}