A polygon with four sides is such that any two adjacent angles are supplementary. At least one pair of opposite angles are supplementary too. Which BEST describes the polygon based on the information given? The Answer is Rectangle. I want to know how through diagram, please explain. Please don't answer of you don't know.
Answers
Let the two adjacent angles be 'x' and'x'.
x + x = 180°
2x = 180°
x = 180°/2
x = 90°
Both the adjacent angles are of = 90° and 90°.
One pair of opposite angles are supplementary.
2 angles we already founded and the polygon has 4 sides means 4 angles.
This means the pair of opposite angles has 1 of the angles of the 90° pair.
Now one the opposite angle we have found, let the other one be 'x'.
Sum of opposite angles = 180°
= x + 90° = 180°
= x = 180° - 90°
= x = 90°
Now we found the 3 angles of the polygon.
We know that the sum of all angles of a polygon is 360°.
Now let us find the 4th angle of the polygon.
Let the 4th angle be 'n'.
90° + 90° + 90° + x° = 360°
270° + n = 360°
n = 360° - 270°
n = 90°
= All angles are of 90°.
ANSWER = Square or Rectangle
____________________________________________
Hope my answer helped.........
Plzz mark me brainliest................
Answer:
polygon
Step-by-step explanation: