In a parallelogram abcd,if angle a =(2x+25) and angle b = (3x_5),find the value of x and the measures of each angle of the parallelogram
The opposite angles are equal:
A = C = 2x+25, B = D = 3x-5.
2(2x+25) + 2(3x-5) = 360.
4x+50 + 6x-10 = 360, X = 32.
A = C = 64+25 = 89o, B = D = 96-5 = 91.
To find the value of x and the measures of each angle of the parallelogram, we can use the properties of parallelograms.
In a parallelogram, the opposite angles are equal. So, angle A is equal to angle C, and angle B is equal to angle D.
Given that angle A is (2x+25) and angle B is (3x-5), we can set up the following equation:
(2x+25) = (3x-5)
Now, we can solve this equation to find the value of x:
2x + 25 = 3x - 5
-5 - 25 = 3x - 2x
-30 = x
So, x is equal to -30.
Now, we can substitute the value of x back into the equation to find the measures of each angle:
Angle A = 2x + 25
Angle A = 2(-30) + 25
Angle A = -60 + 25
Angle A = -35
Angle B = 3x - 5
Angle B = 3(-30) - 5
Angle B = -90 - 5
Angle B = -95
Since angle A is equal to angle C, and angle B is equal to angle D, the measures of each angle of the parallelogram are as follows:
Angle A = Angle C = -35 degrees
Angle B = Angle D = -95 degrees