Answer:
D) 144°
Step-by-step explanation:
In a parallelogram, consecutive angles (those that are adjacent to each other) are supplementary, meaning the sum of their measures is 180°. Therefore:
[tex]m\angle P + m\angle S = 180^{\circ}[/tex]
Given that m∠P = 12a° and m∠S = 3a°, we can substitute these values into the sum equation and solve for a:
[tex]12a^{\circ} + 3a^{\circ} = 180^{\circ}\\\\12a + 3a = 180\\\\15a = 180\\\\a = 12[/tex]
To find the measure of angle P, we can substitute the found value of a into the angle expression:
[tex]m\angle P = 12(12)^{\circ}\\\\m\angle P = 144^{\circ}[/tex]
Therefore, the measure of angle P:
[tex]\LARGE\boxed{\boxed{m\angle P = 144^{\circ}}}[/tex]
