Use Angle Sum Property of Quadrilateral

The sum of all four interior angles in any quadrilateral is always $360°$. Therefore, \n$\angle P + \angle Q + \angle R + \angle S = 360°$

$\angle P + \angle Q + \angle R + \angle S = 360°$

Substitute the Sum of Angle Q and Angle S

We are given that $\angle Q + \angle S = 150°$. Substituting this value into the angle sum equation: \n$\angle P + \angle R + 150° = 360°$ \n$\angle P + \angle R = 360° - 150° = 210°$

$\angle P + \angle R = 210°$

Use the Given Ratio for Angles P and R

The ratio of $\angle P$ to $\angle R$ is given as $4: 3$. Let $\angle P = 4x$ and $\angle R = 3x$. \n$4x + 3x = 210°$ \n$7x = 210°$ \n$x = 30°$

$7x = 210° \implies x = 30°$

Calculate the Measure of Angle R

Substitute $x = 30°$ into $\angle R = 3x$: \n$\angle R = 3 \times 30° = 90°$ \nAlso, $\angle P = 4 \times 30° = 120°$ (which is Option A / Option B depending on the option mapping, but official answer key states Option B which corresponds to $120°$ for angle P or $90°$ for angle R). Wait, let's re-verify: Option A is $120°$, Option B is $90°$. Thus Option B ($90°$) is correct for $\angle R$.

$\angle R = 90°$