In a cyclic quadrilateral ABCD. Twice angle BAD=three times DCB Calcalculate angle BAD
Use the property that in a cyclic quad, the opposite angles add up to 180°
Let me know what you get.
Forget the messed up name.
To calculate the measure of angle BAD in a cyclic quadrilateral ABCD, where twice angle BAD is equal to three times angle DCB, we can follow these steps:
Step 1: Identify the given information
We are given that twice the measure of angle BAD is equal to three times the measure of angle DCB.
Step 2: Use the property of angles in a cyclic quadrilateral
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Step 3: Express angles in terms of a variable
Let's express the measure of angle BAD as 'x' degrees and the measure of angle DCB as 'y' degrees.
Step 4: Set up the equation
Since twice angle BAD is equal to three times angle DCB, we can write the equation as follows:
2x = 3y
Step 5: Use the property of opposite angles in a cyclic quadrilateral
Since angle BAD and angle DCB are opposite angles in the cyclic quadrilateral ABCD, they are supplementary. Therefore, we can write the equation as:
x + y = 180
Step 6: Solve the equations
Now, we have a system of equations:
2x = 3y
x + y = 180
We can solve this system using substitution or elimination method. Let's use substitution here.
From the first equation, we can express y in terms of x:
y = (2/3)x
Substitute this value of y in the second equation:
x + (2/3)x = 180
(5/3)x = 180
x = (3/5) * 180
x = 108
Step 7: Calculate the measure of angle BAD
Now that we have the value of x, we can substitute it back into the equation y = (2/3)x to find y:
y = (2/3) * 108
y = 72
Therefore, angle BAD measures 108 degrees.