Question

3.a)in the diagram below, line & is parallel to line m, and line w is a transversal. If m 2 = 3x + 17 and m/3 = 5x -21, what is mZ1? W 3 →l 2 m m 1

Answer 1

According to the given diagram, angles 2 and 3 are supplementary, which means that the sum of their measures is 180. Use this information to find x:

`\begin{gathered} m\measuredangle2+m\measuredangle3=180 \\ 3x+17+5x-21=180 \\ 8x-4=180 \\ 8x=184 \\ x=(184)/(8) \\ x=23 \end{gathered}`

According to the given diagram we also know that angle 1 and 2 are corresponding, which means that they have the same measure. Using the value of x and the expression for m<2 we can find the measure of angle 1:

`\begin{gathered} m\measuredangle1=m\measuredangle2 \\ m\measuredangle1=3x+17 \\ m\measuredangle1=3\cdot23+17 \\ m\measuredangle1=86 \end{gathered}`

The answer is 86°.