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

What is the value of x in the figure shown below?
Transcript text: What is the value of $x$ in the figure shown below?
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Solution

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Solution Steps

Step 1: Analyze the given figure

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

Step 2: Properties of a parallelogram

In a parallelogram, opposite angles are equal. Thus, DAB=DCB=69\angle DAB = \angle DCB = 69^{\circ} and ABC=ADC\angle ABC = \angle ADC. Also, adjacent angles are supplementary, which means their sum is 180180^{\circ}. Therefore, DAB+ABC=180\angle DAB + \angle ABC = 180^{\circ}.

Step 3: Calculate the value of x

We have DAB+ABC=180\angle DAB + \angle ABC = 180^{\circ}. 69+(43+x)=18069^{\circ} + (43^{\circ} + x^{\circ}) = 180^{\circ} 69+43+x=18069^{\circ} + 43^{\circ} + x^{\circ} = 180^{\circ} 112+x=180112^{\circ} + x^{\circ} = 180^{\circ} x=180112x^{\circ} = 180^{\circ} - 112^{\circ} x=68x^{\circ} = 68^{\circ}

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

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