Determine the value of x in the diagram X
The Correct Answer and Explanation is:
Correct Answer:
x = 144
Explanation:
- Identify the Shape and its Properties:
The diagram shows a quadrilateral with two pairs of parallel sides, indicated by the arrow markings. A quadrilateral with two pairs of parallel sides is a parallelogram. A key property of a parallelogram is that its consecutive interior angles are supplementary, meaning they add up to 180 degrees. Also, opposite angles are equal. - Analyze the Angles:
The diagram provides expressions for the angles in terms of a variable x.- One interior angle is given as x°.
- Another angle is given as (x/4)°. This value is used to label an exterior angle, which is vertically opposite to an interior angle. This means one of the interior angles of the parallelogram is (x/4)°.
- Set Up the Equation:
In a parallelogram, there are two pairs of equal angles. The angles x° and (x/4)° are clearly intended to be the two different angle measures in the parallelogram. As seen in the diagram, one angle (x°) is obtuse (greater than 90°) and the other ((x/4)°) is acute (less than 90°). These must be consecutive angles.Since consecutive angles in a parallelogram are supplementary, we can set up the following equation:
x + x/4 = 180 - Solve the Equation for x:
To solve for x, we first need to combine the terms on the left side of the equation.- Find a common denominator: (4x/4) + (x/4) = 180
- Add the fractions: 5x/4 = 180
- To isolate x, multiply both sides by 4: 5x = 180 * 4
- 5x = 720
- Finally, divide both sides by 5: x = 720 / 5
- x = 144
Conclusion:
The value of x is 144. This means the two consecutive angles of the parallelogram are 144° and (144/4)° = 36°. Their sum is 144° + 36° = 180°, which confirms our use of the supplementary angles property.
