Question

Main Street is a straight road that runs through the center of town. Sycamore Street and Rosewood Street both intersect Main Street at the same angle. Sycamore intersects Main Street at an obtuse angle with measure (9x - 5)degrees. Rosewood Street intersects Main Street at an acute angle with measure (4x + 3)degrees, sketch the roads. What are the measures of the given angles these streets make with Main street?

Answer 1

121 degrees and 59 degrees respectively.

Step-by-step explanation:

The sketch of the roads is attached below:

If Sycamore Street and Rosewood Street both intersect Main Street at the same angle, it means the angle labeled a above is equal to (9x-5) degrees.

`(4x+3)+a=180^0\text{ (Linear Pairs)}`

Since a=(9x - 5) degrees.

`\begin{gathered} (4x+3)+(9x-5)=180 \\ 13x-2=180^0 \\ 13x=180^0+2^0 \\ 13x=182^0 \\ x=(182^0)/(13) \\ x=14^0 \end{gathered}`

Therefore, the measure of the given angles these streets makes with Main Street are:

`\begin{gathered} (9x-5)^0=9(14)-5=121^0 \\ (4x+3)^0=4(14)+3=59^0 \end{gathered}`