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What is the proof to show that sum of either pair of opposite angles in a cyclic quadrilateral is 180 degrees?
Wiki User
∙ 11y ago
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
Wiki User
∙ 11y ago
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What are the opposite angles of a quadrilateral inscribed in a circle?
A quadrilateral is inscribed in a circle it means all the vertices of quadrilateral are touching the circle. therefore it is a cyclic quadrilateral and sum of the opposite angles in cyclic quadrilateral is supplementary. suppose if one angle is A then another will be 180 degree - angle A.
How cyclic integral of a point function is zero?
the cyclic integral of this is zero
Is every finite abelian group is cyclic?
No, for instance the Klein group is finite and abelian but not cyclic. Even more groups can be found having this chariacteristic for instance Z9 x Z9 is abelian but not cyclic
Construct a systematic 7 4 cyclic code using generator polynomial?
So I believe you mean to say 4 7? Because cyclic codes never start with 7. The answer is 42 by the way.
What is finite and infinite cyclic group?
Normally, a cyclic group is defined as a set of numbers generated by repeated use of an operator on a single element which is called the generator and is denoted by g.If the operation is multiplicative then the elements are g0, g1, g2, ...Such a group may be finite or infinite. If for some integer k, gk = g0 then the cyclic group is finite, of order k. If there is no such k, then it is infinite - and is isomorphic to Z(integers) with the operation being addition.
Is every square cyclic?
Yes. The sum of opposite angles is 180 degrees and that is a necessary and sufficient condition for a quadrilateral to be cyclic.
Is a rectangle a cyclic quadrilateral?
yes rectangle is a cyclic quadrilateral because its all angles are 90. so adiing opposite angles is 180.
What are supplementary angles that are NOT a linear pair?
Any two angles whose measures add up to 180 degrees. For example, opposite angles of a cyclic quadrilateral (quadrilateral whose vertices are on a circle).
What are the properties of a cyclic quadrilateral?
A cyclic quadrilateral is one that has concyclic vertices (its corners all fit on the same circle) and, for a simple cyclic quadrilateral, opposite angles are supplementary.
What is a cylic quadrilateral?
A cyclic quadrilateral is one where the sum of measures of opposite angles is 180 degrees. I t mostly is formed with the vertices as part of the circumference of a circle.
What are the opposite angles of a quadrilateral inscribed in a circle?
A quadrilateral is inscribed in a circle it means all the vertices of quadrilateral are touching the circle. therefore it is a cyclic quadrilateral and sum of the opposite angles in cyclic quadrilateral is supplementary. suppose if one angle is A then another will be 180 degree - angle A.
What is the formula of finding the interior angles of a quadrilateral?
IF it is a cyclic quadrilateral (all four vertices on one circle), then opposite angles add to 180 degrees. So knowing one will enable you to find the other. The sum of the four angles is 360 degrees. So if you know three you can work out the fourth.
Does the quadrilateral have any supplementary angles?
Depends on the quadrilateral. Eg in a cyclic Quad, opposite angles are supplementary. Note that it is impossible that there would be only one pair of supp. angles as the internal angles total 360o
The rules of a cyclic Quadrilateral?
In geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. The vertices are said to be concyclic. In a cyclic quadrilateral, opposite angles are supplementary (their sum is π radians or 180°). Equivalently, each exterior angle is equal to the opposite interior angle. The area of a cyclic quadrilateral is given by Brahmagupta's formula as long as the sides are given. This area is maximal among all quadrilaterals having the same side lengths. Ptolemy's theorem expresses the product of the lengths of the two diagonals of a cyclic quadrilateral as equal to the sum of the products of opposite sides. In any convex quadrilateral, the two diagonals together partition the quadrilateral into four triangles; in a cyclic quadrilateral, opposite pairs of these four triangles are similar to each other. Any square, rectangle, or isosceles trapezoid is cyclic. A kite is cyclic if and only if it has two right angles. ----Wikipedia
What are the properties of a Quadrilateral within a circle?
If you mean a Quad which touches the circumference at all 4 points, then... # All interior angles add to 360' #Opposite angles add to 180' #The Quad is then referred to as a 'Cyclic Quadrilateral'
How do you find the radius of a rhombus?
A rhombus cannot be a cyclic quadrilateral because its opposite angles are not supplementary (unless it is a square). It cannot, therefore, have a radius.
Is all rectangles cyclic?
as the sum of opposite angles of a rectangle always equals 180 degrees all rectangles are cyclic Actually a rectangle is only cyclic when the product of the diagonls equals the sum of opposite pairs of sides.
