Question

the interior angles of every triangle, regardless of their dimensions, add up to 180 °. select one: true false in the parallelogram below, if < a = 47 degrees, and < c = 8x + 15 degrees, find x. select one: a. 5 b. 4 c. 12

Explanation:

Step1: Evaluate triangle angle statement

The sum of interior angles of any triangle is a fundamental geometric fact equal to $180^\circ$.

Step2: Set up parallelogram angle equation

In a parallelogram, opposite angles are equal. So $\angle A = \angle C$, giving:
$47 = 8x + 15$

Step3: Solve for x

Subtract 15 from both sides:
$47 - 15 = 8x$
$32 = 8x$
Divide by 8:
$x = \frac{32}{8} = 4$

Answer:

1. True
2. b. 4