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What is a parallelogram with one interior angle equal to 90?
It is a square, a regular parallelogram with all right angles. The reason is that in a parallelogram, the adjacent angles are supplementary (equal 180 degrees).In any case, the opposite angle would be 90 degrees as well, leaving just 180 degrees for the other two identical opposite angles.
Are all angles of a parallelogram equal to 90 degrees?
No, only in a square (regular parallelogram).The opposite angles are EQUAL in a parallelogram, and the adjacent angles are SUPPLEMENTARY(they equal 180 degrees).So if any angle in a parallelogram is a right angle, they all are. Otherwise, there are no right angles.The angles of a parallelogram will average 90 degrees, as there are 360 degrees in any quadrilateral, (360/4 - 90) and 180 degrees in two adjacent non-equal angles (180/2 = 90).
The opposite angles of a quadrilateral inscribed in a circle are?
The opposite angles of a quadrilateral inscribed in a circle are supplementary, meaning they add up to 180 degrees. This is due to the property that the sum of the opposite angles of any quadrilateral inscribed in a circle is always 180 degrees. This property can be proven using properties of angles subtended by the same arc in a circle.
What is the proof to show that sum of either pair of opposite angles in a cyclic quadrilateral is 180 degrees?
Because the 4 interior angles of any quadrilateral add up to 360 degrees and a cyclic quadrilateral diagonals opposite angles add up to 180 degrees therefore it follows that the other pair must be 180 degrees
What are the angles in a parallelogram if the measure of one interior angle is 50 degrees more than 4 times the measure of another angle?
Opposite angles of a parallelogram are equal, and adjacent angles are supplementary. Let one angle be θ, then the adjacent angle is 4θ + 50° → θ + 4θ + 50° = 180° → 5θ = 130° → θ = 26° → The two adjacent angles are 26° and 154°. → The angles of the parallelogram are 26°, 154°, 26°, 154°.
