16.
EBC=90 because is a rigth angle
so we just need DBE
we know
[tex]\begin{gathered} \text{ABD}+\text{DBE}=\text{ABE} \\ \text{ABD}+\text{DBE}=90 \end{gathered}[/tex]
because ABE is a rigth angle
and we know the value of ABD, is 30
so we can replace to find DBE
[tex]\begin{gathered} 30+\text{DBE}=90 \\ \text{DBE}=90-30 \\ \text{DBE}=60 \end{gathered}[/tex]
now
[tex]\begin{gathered} \text{DBC}=\text{EBC}+\text{DBE} \\ \text{DBC}=90+60 \\ \text{DBC}=150 \end{gathered}[/tex]
the measure is 150Degrees
17.
use the same method
we know
[tex]ABF=\text{EBF}+\text{ABE}[/tex]
ABE=90 because is a rigth angle
to calculate EBF:
[tex]\begin{gathered} \text{EBF}=\text{EBC-FBC} \\ \text{EBF}=90-40 \\ \text{EBF}=50 \end{gathered}[/tex]
we know EBC=90 because is a rigth angle and FBC=40 is on the exercise
we replace EBF on
[tex]\begin{gathered} \text{ABF}=\text{EBF}+\text{ABE} \\ \text{ABF}=50+90 \\ \text{ABF}=140 \end{gathered}[/tex]
the measure of ABF is 140 degrees
