Questions: What is the value of x in the figure shown below?

Solution Steps

We are given a parallelogram $ABCD$ with $AB = CD = 4.3$ and $AC = BD = 3$. Also, we are given $\angle DAB = 69^{\circ}$ and $\angle ABC = 43^{\circ} + x^{\circ}$. We need to find the value of $x$.

In a parallelogram, opposite angles are equal. Thus, $\angle DAB = \angle DCB = 69^{\circ}$ and $\angle ABC = \angle ADC$. Also, adjacent angles are supplementary, which means their sum is $180^{\circ}$. Therefore, $\angle DAB + \angle ABC = 180^{\circ}$.

We have $\angle DAB + \angle ABC = 180^{\circ}$. $69^{\circ} + (43^{\circ} + x^{\circ}) = 180^{\circ}$ $69^{\circ} + 43^{\circ} + x^{\circ} = 180^{\circ}$ $112^{\circ} + x^{\circ} = 180^{\circ}$ $x^{\circ} = 180^{\circ} - 112^{\circ}$ $x^{\circ} = 68^{\circ}$

Final Answer The final answer is $\boxed{68}$