Given parallelogram abcd prove < a and < b are supplementary.< b and < c are supplementary

1. Quadrilateral ABCD is a parallelogram     Given

2. AB||DC and AD||BC                         Opposite sides of a parallelogram are parallel.

3. <A and <B are same side interior angles   Definition of a parallelogram.

<B and < C  are same side interior angles

4) m <A + m<B = 180 degrees  Same side angles of a parallelogram are of 180°

m<B + m<C = 180 degrees.

5) <A and <B are supplementary

<B and <C are supplementary                  Definition of supplementary angles.

we don't have enough info to solve this

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.