if opposite angles of cyclic quadrilateral are in the ratio 2:3 then find the measure of all angles
In a cyclic quad, opposite angles must add up to 180°
let the angles be 2x and 3x
so 5x = 180
x = 36
The two angles are 72° and 108°.
More information is needed to find the remaining two angles.
Good
2x+3x=180
5x=180
X=36
2(36)=72 & 3(36)=108
its difficult to understand with explanation
Well, isn't that a wheel-y interesting question! Let's unwrap this puzzle, shall we?
In a cyclic quadrilateral, the opposite angles add up to 180 degrees. So let's call the angles 2x and 3x.
Since the opposite angles are in a 2:3 ratio, we can set up the equation 2x + 3x = 180 degrees.
Combining like terms, we have 5x = 180 degrees.
Now, let's solve for x. Dividing both sides of the equation by 5, we find that x = 36 degrees.
So, the measure of the angles will be:
Angle 1: 2x = 2 * 36 = 72 degrees
Angle 2: 3x = 3 * 36 = 108 degrees
Angle 3: 2x = 72 degrees
Angle 4: 3x = 108 degrees
And there you have it! The measure of all the angles in the cyclic quadrilateral. Keep rolling with those math questions!
To find the measures of all angles in a cyclic quadrilateral, we can use the property that opposite angles in a cyclic quadrilateral are supplementary, meaning they add up to 180 degrees.
Let's denote the opposite angles as A, B, C, and D, where A and C are the smaller angles, and B and D are the larger angles.
According to the given information, the ratio of the opposite angles is 2:3. This means that we can write the following equation based on the proportion:
A : B = 2 : 3
To solve this equation and find the specific angles, we need to assign a variable to one of the angles. Let's say A = 2x.
Using the ratio, we can determine that B = 3x.
Since opposite angles are supplementary, A + B = 180 degrees. Substituting the values of A and B:
2x + 3x = 180
5x = 180
Solving for x:
x = 180 / 5
x = 36
Now that we have the value of x, we can find the measures of all the angles:
A = 2x = 2 * 36 = 72 degrees
B = 3x = 3 * 36 = 108 degrees
Since opposite angles in a cyclic quadrilateral are congruent (equal in measure), we can conclude that C = A = 72 degrees and D = B = 108 degrees.
Therefore, the measures of all the angles in the cyclic quadrilateral are:
Angle A = 72 degrees
Angle B = 108 degrees
Angle C = 72 degrees
Angle D = 108 degrees