Question

R is perpendicular to U. S is parallel to T. m <1 = 39° . Find the remaining angles.

Answer 1

First, notice that angle 1 and angle 4 are vertical angles, therefore:

`\measuredangle1=39\text{ = }\measuredangle4`

then, we have that angle 1 and angle 2 are supplemetary angles, then:

`\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \Rightarrow\measuredangle2=180-\measuredangle1=180-39=141 \\ \measuredangle2=141 \end{gathered}`

Since angle 3 and angle 2 are vertical, we have the first measures of the diagram:

`\begin{gathered} \measuredangle1=39 \\ \measuredangle2=141 \\ \measuredangle3=141 \\ \measuredangle4=39 \end{gathered}`

Then, angle 1 and angle 5 are corresponding angles, then, we have the following:

`\measuredangle1=39=\measuredangle5`

Now, angle 5 and angle 6 are complementary angles, therefore:

`\begin{gathered} \measuredangle5+\measuredangle6=90 \\ \Rightarrow\measuredangle6=90-\measuredangle5=90-39=51 \\ \measuredangle6=51 \end{gathered}`

Angle 5 is vertical with angle 7, and angle 6 is vertical with angle 8. Also, we can see that angle 9 is a right angle, then, we have the next measures:

`\begin{gathered} \measuredangle5=39 \\ \measuredangle6=51 \\ \measuredangle7=39 \\ \measuredangle8=51 \\ \measuredangle9=90 \end{gathered}`

Finally, notice that angles 4, 9 and 10 are the angles of a right triangle, then, we would have the following:

`\begin{gathered} \measuredangle4+\measuredangle9+\measuredangle10=180 \\ \Rightarrow\measuredangle10=180-\measuredangle9-\measuredangle4=180-90-39=51 \\ \measuredangle10=51 \end{gathered}`

then, angle 10 and angle 11 are supplemetary, then:

`\begin{gathered} \measuredangle10+\measuredangle11=180 \\ \Rightarrow\measuredangle11=180-\measuredangle10=180-51=129 \\ \measuredangle11=129 \end{gathered}`

angle 10 is vertical with angle 13 and angle 11 is vertical with angle 12, then:

`\begin{gathered} \measuredangle10=51 \\ \measuredangle11=129 \\ \measuredangle12=129 \\ \measuredangle13=51 \end{gathered}`