here are two triangles
it is given that two angles are congruent so this one must also be since all angles a+b+c =180
so therefor c of angle A and c of angle B must be congruent
third angle=y
2y+23+=5y-13
2y+(23+13)=5y+(13-13)
2y+36=5y
(2y-2y)+36=5y-2y
36=3y
36/3=3y/3
12=y
y=12
now for x
since these triangles have congruent angles their sides must be similar
it is already given that both triangles have within itself 2 congruent sides
so in triangle A
it shows that in triangle A
side a= 8
side b=18
side c is not given however it is congruent to side b
side b= side c
side c=18
now for triangle B since these are similar triangles
and its given that two sides are equal lets figure out the value of x
since in triangle A: 18+18+8=44
triangle B (2x+3)2+20=?
since these triangles are similar
side a:a
side b:b
side c:c
so if we have a given of 20:8
20/8=2.5
so 18(2.5)=2x+3
18(2.5)=2x+3
18*2.5=45
45=2x+3
45-3=2x+(3-3)
42=2x
42/2=2x/2
21=x
therefor
x=21
x=21 , y=12
