Question

Please some help with 16 and 17 problems I need a explanation

Answer 1

16.

EBC=90 because is a rigth angle

so we just need DBE

we know

`\begin{gathered} \text{ABD}+\text{DBE}=\text{ABE} \\ \text{ABD}+\text{DBE}=90 \end{gathered}`

because ABE is a rigth angle

and we know the value of ABD, is 30

so we can replace to find DBE

`\begin{gathered} 30+\text{DBE}=90 \\ \text{DBE}=90-30 \\ \text{DBE}=60 \end{gathered}`

now

`\begin{gathered} \text{DBC}=\text{EBC}+\text{DBE} \\ \text{DBC}=90+60 \\ \text{DBC}=150 \end{gathered}`

the measure is 150Degrees

17.

use the same method

we know

`ABF=\text{EBF}+\text{ABE}`

ABE=90 because is a rigth angle

to calculate EBF:

`\begin{gathered} \text{EBF}=\text{EBC-FBC} \\ \text{EBF}=90-40 \\ \text{EBF}=50 \end{gathered}`

we know EBC=90 because is a rigth angle and FBC=40 is on the exercise

we replace EBF on

`\begin{gathered} \text{ABF}=\text{EBF}+\text{ABE} \\ \text{ABF}=50+90 \\ \text{ABF}=140 \end{gathered}`

the measure of ABF is 140 degrees