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
To find the value of x and the measures of each angle of the parallelogram, we can use the property that opposite angles in a parallelogram are equal.
Given that angle A is equal to (2x + 25) and angle B is equal to (3x - 5), we can set up an equation:
A = B
(2x + 25) = (3x - 5)
Now, solve for x:
2x + 25 = 3x - 5
25 + 5 = 3x - 2x
30 = x
So, x = 30.
To find the measures of each angle, substitute the value of x back into the expressions for angles A and B:
Angle A = 2x + 25 = 2(30) + 25 = 60 + 25 = 85 degrees
Angle B = 3x - 5 = 3(30) - 5 = 90 - 5 = 85 degrees
Since opposite angles in a parallelogram are equal, angles C and D will also measure 85 degrees.
Therefore, the value of x is 30, and each angle of the parallelogram measures 85 degrees.