Question

in parallelogram abcd, what is the value of angle a?
a b
(2x + 3)°
(6x - 15)°
d c
51°
156°
24°
129°

Explanation:

Step1: Use parallelogram consecutive angles property

Consecutive angles in a parallelogram are supplementary, so:
$$(2x + 3) + (6x - 15) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$8x - 12 = 180$$
$$8x = 192$$
$$x = 24$$

Step3: Find $\angle B$ first

Substitute $x=24$ into $\angle B$ expression:
$$\angle B = 2(24) + 3 = 51^\circ$$

Step4: Find $\angle A$ using supplementary property

$\angle A$ and $\angle B$ are consecutive angles:
$$\angle A = 180^\circ - 51^\circ = 129^\circ$$

Answer:

129°