Question

Find the measure of all the angles if m<2 = 76°

Answer 1

`m2\measuredangle=76º`

By opposite angles we know that:

`\begin{gathered} m1\measuredangle=m3\measuredangle \\ m2\measuredangle=m4\measuredangle \\ m5\measuredangle=m7\measuredangle \\ m8\measuredangle=m6\measuredangle \end{gathered}`

By corresponding angles we know that

`\begin{gathered} m5\measuredangle=m1\measuredangle \\ m2\measuredangle=m6\measuredangle \\ m4\measuredangle=m8\measuredangle \\ m7\measuredangle=m3\measuredangle \end{gathered}`

by complementary angles we know that

`\begin{gathered} m1\measuredangle+m2\measuredangle=180º \\ m1\measuredangle+76º=180º \\ m1\measuredangle=104º \end{gathered}`

Using the correspondence and opposite angles:

`\begin{gathered} m1\measuredangle=m3\measuredangle=m5\measuredangle=m7\measuredangle=104º \\ m2\measuredangle=m4\measuredangle=m6\measuredangle=m8\measuredangle=76º \end{gathered}`