Question

4
if abcd is a parallelogram, what is the value of x?

a. 37
b. 46
c. 38
d. 82
e. 69
f. 44

Explanation:

Step1: Recall properties of parallelograms

In a parallelogram, consecutive angles are supplementary (their sum is \(180^\circ\)). Here, \(\angle A = 42^\circ\) and \(\angle D=(3x + 6)^\circ\) are consecutive angles, so they should add up to \(180^\circ\).

Step2: Set up the equation

We set up the equation based on the supplementary angles property: \(42+(3x + 6)=180\).

Step3: Simplify the left - hand side

First, combine like terms: \(42 + 6+3x=180\), which simplifies to \(48+3x = 180\).

Step4: Solve for x

Subtract 48 from both sides of the equation: \(3x=180 - 48\). So, \(3x = 132\). Then divide both sides by 3: \(x=\frac{132}{3}=44\).

Answer:

F. 44