Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°. Statement Reason
Points A, B, and C form a triangle. given
Let be a line passing through B and parallel to . definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4
m∠1 = m∠4 and m∠3 = m∠5
m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° substitution

m a t h w a y. c o m

step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

step-by-step explanation:

options

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8