∆abe ~ ∆tcd, m∠a = 61°, and m∠c = 55° m∠d =

m∠D = 64°

Step-by-step explanation:

the measure of third angle = the sum of the interior angles - the sum of two angles

the sum of the interior angles of a triangle is 180°

180 - (61 + 55) = 64

so ∠D = 64°

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.