Question

The walking paths at a park meet eachother as shown. What is the measure of the angle between the second path and third Path?

Answer 1

41.25°

Explanation:

Second path ahd third path intersecting form the angle with measure 3x-1.

Three angles 3x-1, 9x-7 and 19° together form straight angle. Hence,

`3x-1+9x-7+19^(\circ)=180^(\circ),\\ \\12x=180-19+8,\\ \\12x=169^(\circ),\\ \\x=(169)/(12)^(\circ).`

Now the angle between the second and third paths is

`3x-1=3\cdot (169)/(12)-1=(169)/(4)-1=(169-4)/(4)=(165)/(4)=41.25^(\circ)`