In a trapezium ABCD,ABperpendicular DC.if angle A=4x degree,angle B=(6x+10degree),angle C=(3x-10degree) & angle D=5x degree.find each angle of trapezium.

To find the measures of each angle in the trapezium ABCD, we need to use the given information that AB is perpendicular to DC.

Let's solve for the value of x first:

Since AB is perpendicular to DC, angle A and angle D are complementary angles (they add up to 90 degrees).

So, we have the equation: 4x + 5x = 90 degrees.

Simplifying the equation, we get: 9x = 90 degrees.

Dividing both sides by 9, we find: x = 10 degrees.

Now, let's substitute the value of x back into the given angle measures to find the measures of each angle:

Angle A = 4x = 4 * 10 = 40 degrees

Angle B = 6x + 10 = 6 * 10 + 10 = 60 + 10 = 70 degrees

Angle C = 3x - 10 = 3 * 10 - 10 = 30 - 10 = 20 degrees

Angle D = 5x = 5 * 10 = 50 degrees

Therefore, the measures of the four angles in the trapezium ABCD are:

Angle A = 40 degrees
Angle B = 70 degrees
Angle C = 20 degrees
Angle D = 50 degrees