ratios of opposite angles of a cyclic quadrilateral is 5:4 find the angle
100&80
the ratio of opposite sides of cyclic quadrilateral is 5:7 what is the messure of two angles
To find the angle of a cyclic quadrilateral when the ratios of opposite angles are given, you can follow these steps:
Step 1: Understand the concept
In a cyclic quadrilateral, opposite angles are supplementary, meaning they add up to 180 degrees. If the ratios of opposite angles are known, you can set up an equation and solve for the variables.
Step 2: Assign variables
Let the angles of the cyclic quadrilateral be represented by variables. For example, let's use 'x' for one angle and 'y' for the opposite angle.
Step 3: Set up the equation
From the given information, the ratio of opposite angles is 5:4. This means that for every 5 parts of an angle, there are 4 parts of the opposite angle. You can set up the equation as follows:
5x = 4y
Step 4: Use additional information
To solve the equation, you may need additional information. For example, if you know the sum of all angles in a quadrilateral is 360 degrees, you can use that to obtain another equation.
Step 5: Solve the equation
Solve the equation using the information you have. In this case, we can consider the sum of all angles in a quadrilateral. The sum of all angles is 360 degrees, so you can set up another equation:
x + y + x + y = 360
Step 6: Solve for the variables
Now, you have two equations:
5x = 4y
x + y + x + y = 360
You can solve these equations simultaneously to find the values of 'x' and 'y', which represent the angles of the cyclic quadrilateral.
Once you have found the values of 'x' and 'y', you can determine the actual angle by substituting the values back into the equation(s).