Answer:
[tex]55^0[/tex]
Step-by-step explanation:
Hello,
let's note e the angle that we are looking for
We know that in a triangle the sum of angles is 180 so we can write
For the BDE triangle
(1) 4x + 5x -1 + e = 180 <=> 9x + e - 1 =180
for the ACE triangle
(2) 4x + 6x-15 + e = 180 <=> 10x + e -15 = 180
So (2)-(1) gives
10x + e -15 - (9x + e - 1 ) = 180 - 180 = 0
<=> 10x + e -15 -9x -e +1 = 0
<=> x -14 = 0
<=> x = 14
and then we replace in (2) it comes
10*14 + e - 15 = 180
<=> 140 + e - 15 = 180
<=> e = 180 + 15 - 140 = 40 + 15 = 55
so m<E = [tex]55^0[/tex]
Hope this helps
