Question

in the given figure, l || m and
t is a transversal. The angle bisectors of
wrior angles intersect at P and Q. Find the value of x and y.​

Answer 1

Answer:

x=y=90

Step-by-step explanation:

we know that  <abc=180

          =>   <abe+<cbe=180

           =>       2<pbe+2<ebq=180         [pb bisects <abe and bq bisects ebc]

          =>     <pbe+<ebq=90

        =>         <pbq=90

Similarly,       <peq=90

        in pbqe,

<p+<b+<q+<e=360

=> 90+90+<p+<q=360

=> <p+<q=180         [eq 1]

also, <abe=<bef    [alternate interior angle]

  =>    2<pbe=2<beq

      =>   <pbe=<beq

=>    pb||eq

similarly, bq||pe

=>pbqe is a ||gram

=>   <p=<q

=> <bpe=<bqe                   [vertical opposite]

=>     y=x=90                      [from eq 1]