Question

In the first pic ABC=DBE find value of x, ABC=DEF find F in the second one

Answer 1

if ABC = DBE

then <a = <d and <c = <e

<c = <e

<c = 83

<a +<b + <c = 180  triangles add to 180

x+8 + 51+ 83 = 180

combine like terms

x+142 = 180

subtract 142 from each side

x = 38

ABC = DEF

then  <a = <d  <b = <e   and <c = <f

125 = <e

<d+<e+ <f = 180  triangles add to 180

35+125+ <f = 180

combine like terms

160 +<f = 180

subtract 160 from each side

<f = 120

Answer 2

First problem:

x + 8 + 51 + 83 = 180

x + 142 = 180

x = 38

Second problem:

m<C + 35 + 125 = 180

m<C + 160 = 180

m<C = 20

m<F = m<C = 20