Question

Can you find the measure of the indicated angle and type the correct code?

Answer 1

To identify the different angles of the 4 exercises of hte Puzzle #4 we must find the value of x in each of them, for this we will use the following image to identify the equal angles.

From the image we can see that all the yellow angles resemble each other and the green ones the same

1)

`\begin{gathered} (2x+35)=(8x-49) \\ 8x-2x=35+49 \\ 6x=84 \\ x=(84)/(4) \\ x=14 \end{gathered}`
`\begin{gathered} \measuredangle A=2x+35 \\ \measuredangle A=2(14)+35 \\ \measuredangle A=28+35 \\ \measuredangle A=63º \end{gathered}`

The answer is F

2)

`\begin{gathered} (10x-18)+(15x+48)=180º \\ 10x+15x=180+18-48 \\ 25x=150 \\ x=(150)/(25) \\ x=6 \end{gathered}`
`\begin{gathered} \measuredangle B=15x+48 \\ \measuredangle B=15(6)+48 \\ \measuredangle B=90+48 \\ \measuredangle B=138º \end{gathered}`

The answer is B

3)

`\begin{gathered} (7x+5)=(12x-75) \\ 12x-7x=75+5 \\ 5x=80 \\ x=(80)/(5) \\ x=16 \end{gathered}`

`\begin{gathered} \measuredangle C=7x+5 \\ \measuredangle C=7(16)+5 \\ \measuredangle C=112+5 \\ \measuredangle C=117º \end{gathered}`

The answer is C

4)

`\begin{gathered} (10x+16)+(27x-21)=180 \\ 27x+10x=180+21-16 \\ 37x=185 \\ x=(185)/(37) \\ x=5 \end{gathered}`

`\begin{gathered} \measuredangle D=27x-21 \\ \measuredangle D=27(5)-21 \\ \measuredangle D=135-21 \\ \measuredangle D=114º \end{gathered}`

The answer is A