Question

In the figure shown to the right, two angle measurements are given. Determine the others.

Answer 1

The figure is shown below

From the figure

Angle 150 degree and angle p forms angles on a straight

Since the sum of angles on a straight line equals 180 degrees

Hence

`150^(\circ)+p=180^(\circ)`

Solve for p in the equation

`\begin{gathered} p=180^(\circ)-150^(\circ) \\ p=30^(\circ) \end{gathered}`

Hence, p = 30

From the figure

Angle p and angle q are vertically opposite angles

Since vertically opposite angles are equal then

`p=q=30^(\circ)`

Hence, q = 30

Applying the rule of angles on a straight line

This implies

`q+w+60=180`

Substitute q = 30 into the equation

`30+w+60=180`

Solve for w

`\begin{gathered} w+90=180 \\ w=180-90 \\ w=90 \end{gathered}`

Hence, w = 90