20.4k views
2 votes
If m2 = 12x - 15 and m27 = 3x + 21, what is the measure of 21?

1 Answer

7 votes

In the given figure, m∠2 and m∠7 are "Alternate Exterior Angles" and they are always congruent (equal).

So we can equate them and solve for x.


\begin{gathered} m\angle2=m\angle7 \\ 12x-15=3x+21 \\ 12x-3x=21+15_{} \\ 9x=36 \\ x=(36)/(9) \\ x=4 \end{gathered}

So, m∠2 is


\begin{gathered} m\angle2=12x-15 \\ m\angle2=12(4)-15 \\ m\angle2=48-15 \\ m\angle2=33\degree \end{gathered}

According to the straight-line angle property, the sum of m∠1 and m∠2 must be equal to 180°


\begin{gathered} m\angle1+m\angle2=180\degree \\ m\angle1+33\degree=180\degree \\ m\angle1=180\degree-33\degree \\ m\angle1=147\degree \end{gathered}

Therefore, the measure of m∠1 is 147°

User WantToKnow
by
4.5k points