Question

solve for ( x ) in the parallelogram below.

the parallelogram has angles ( (-3x + 53)^circ ) and ( (-8x + 160)^circ ) marked with blue sectors at the vertices.

Explanation:

Step1: Use parallelogram consecutive angles property

Consecutive angles in a parallelogram are supplementary, so their sum equals $180^\circ$.
$$(-3x + 53) + (-8x + 160) = 180$$

Step2: Combine like terms

Add the variable terms and constant terms.
$$-11x + 213 = 180$$

Step3: Isolate the variable term

Subtract 213 from both sides.
$$-11x = 180 - 213$$
$$-11x = -33$$

Step4: Solve for x

Divide both sides by -11.
$$x = \frac{-33}{-11}$$

Answer:

$x = 3$