Question

modeling real life the map shows the intersections of three roads. malcom way intersects sydney street at an angle of 162°. park road intersects sydney street at an angle of 87°. find the angle at which malcom way intersects park road. malcolm way intersects park road at an angle of °.

Explanation:

Step1: Consider the angles on a straight - line

The sum of angles around a point on a straight - line is 180°. Let the angle between Malcom Way and Park Road be $x$.

Step2: Set up the angle - sum equation

We know that the sum of the three angles formed at the intersection of the three roads (related to Sydney Street) should satisfy the angle - sum property. If we consider the angles formed on Sydney Street, we have $162^{\circ}+x + 87^{\circ}=360^{\circ}$ (since the sum of angles around a point is 360°). But we can also consider the non - reflex angles. The non - reflex angle between Malcom Way and Sydney Street is $180 - 162=18^{\circ}$.

Step3: Calculate the required angle

The angle between Malcom Way and Park Road can be found by considering the non - reflex angles at the intersection. The non - reflex angle between Malcom Way and Sydney Street is $180 - 162 = 18^{\circ}$, and the angle between Park Road and Sydney Street is $87^{\circ}$. Then $x=87^{\circ}-18^{\circ}$.
$x = 69^{\circ}$

Answer:

$69$