Q1)
As shown in the diagram attached, the angle made between 4th street and king avenue if car is traveling from the west side is 75°.
when the car is travelling from the east side and is supposed to take a turn towards north east lets call the angle it makes with the turn as x.
4th street is a straight road, therefore straight line
and sum of angles of a straight line is 180°.x and 75 are supplementary angles.
Therefore x + 75° = 180°
x = 105°
therefore the angle it makes in the turn is 105°
Q2)
When the car is travelling south west and turns left towards 3rd street, the angle it makes is termed as y. when 2 parallel lines are cut by a transversal, x° and y° are corresponding angles.
This means that the angle at which transversal cuts 3rd street and 4th street to the left are both equal. these are called corresponding angles.
this means that x = y
as derived in the previous question, x = 105°,
hence, y = 105°.
Q3)
When the car is travelling north east and turns right onto 3rd street, lets name the angle it makes with the turn as z.
angles y and z are called vertically opposite angles. When 2 straight lines cut each other, the opposite angles formed are equal to each other.
Therefore y = z.
as derived in the previous question y = 105°.
since y = z
hence, z = 105°
