Question

The map shows the intersection 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.

Answer 1

Answer:

The angle  at which malcom Way intersects Park Road = 111 °

Step-by-step explanation:

Malcom Way intersects Sydney Street at $\theta_{1}$ = 162 °

Park Road intersects Sydney Street at $\theta_{2}$ = 87 °

The angle at which Malcom Way intersects Park Road $\theta_{3}$ = ?

We know that

$\theta_{1} + \theta_{2} + \theta_{3} = 360$

$\theta_{3} = 360 - \theta_{1} - \theta_{2}$

$\theta_{3} = 360 - 162 - 87$

$\theta_{3} = 111$ °

Therefore the angle  at which malcom Way intersects Park Road = 111 °