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