Question

find the measure of ∠a in parallelogram abcd.

Explanation:

Step1: Use parallelogram angle property

In a parallelogram, opposite angles are equal, so $\angle A = \angle C$.
Set up equation: $14x + 18 = 12x + 30$

Step2: Solve for $x$

Subtract $12x$ from both sides: $14x - 12x + 18 = 30$
Simplify: $2x + 18 = 30$
Subtract 18 from both sides: $2x = 30 - 18$
Calculate: $2x = 12$
Divide by 2: $x = \frac{12}{2} = 6$

Step3: Calculate $\angle A$

Substitute $x=6$ into $\angle A = 14x + 18$:
$\angle A = 14(6) + 18$
Calculate: $\angle A = 84 + 18 = 102$

Answer:

$102^\circ$