Answer:
AB // CD and AD // BC, then ABCD is a parallelogram
Step-by-step explanation:
Step 2: Show AD // BC
A = (-3 , 3) and D = (0 , 0)
Find the slope of AD
B = (2 , 5) and C = (5 , 2)
The slope of AD = the slope of BC
So AD // BC because they have the same slope
Step 3:
Each two opposite sides are parallel in quadrilateral ABCD
So the quadrilateral is a parallelogram
The value of x is 81
Step-by-step explanation:
The sum of the interior angles of any quadrilateral is 360°
∵ The figure have 4 sides
∴ The figure is a quadrilateral
∵ The sum of the measures of the interior angles of a
quadrilateral is 360°
- Add the four angles and equate the sum by 360
∴ m∠1 + m∠2 + m∠3 + x = 360
∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral
∴ m∠1 = 40% × 360 = × 360 = 144°
∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral
∴ m∠2 = 12.5% × 360 = × 360 = 45°
∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral
∴ m∠3 = 25% × 360 = × 360 = 90°
- Substitute these values in the equation above
∴ 144 + 45 + 90 + x = 360
- Add the like terms in the left hand side
∴ 279 + x = 360
- Subtract 279 from both sides
∴ x = 81°
The value of x is 81
Learn more:
You can learn more about the polygons in brainly.com/question/6281564
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