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.
The angle sum of a trapezium must be 360° , so
4x + 6x+10 + 3x-10 + 5x = 360
18x = 360
x = 20
angle A = 80°
angle B = 130°
angle C = 50°
angle D = 100°
I don't see any perpendicular sides.
Your question contains a contradiction.
Given:
AB is parallel to DC
Angle A = 4x
Angle B = 6x + 10
Angle C = 3x - 10
Angle D = 5x
In a trapezium, the sum of the opposite angles is 180 degrees.
Therefore, we have the following equations:
Angle A + Angle C = 180 (Opposite angles between AB and DC)
4x + 3x - 10 = 180
7x - 10 = 180
7x = 180 + 10
7x = 190
x = 190 / 7
x = 27.142857
Now, we find the value of each angle:
Angle A = 4x = 4 * 27.142857 = 108.571428 degrees
Angle B = 6x + 10 = 6 * 27.142857 + 10 = 162.857142 + 10 = 172.857142 degrees
Angle C = 3x - 10 = 3 * 27.142857 - 10 = 81.428571 - 10 = 71.428571 degrees
Angle D = 5x = 5 * 27.142857 = 135.714285 degrees
Therefore, each angle of the trapezium is as follows:
Angle A = 108.571428 degrees
Angle B = 172.857142 degrees
Angle C = 71.428571 degrees
Angle D = 135.714285 degrees
To find the measure of each angle in the trapezium ABCD, we'll use the given information and the properties of trapeziums:
1. In a trapezium, the opposite angles are supplementary. So, we can set up the following equation:
A + C = 180 degrees
2. In a trapezium, the adjacent angles on the same leg are supplementary. Thus, we can set up the following equation as well:
B + D = 180 degrees
Let's solve these equations to determine the values of the angles:
Given:
AB || DC (AB is parallel to DC)
Angle A = 4x degrees
Angle B = 6x + 10 degrees
Angle C = 3x - 10 degrees
Angle D = 5x degrees
Using the equation A + C = 180 degrees:
4x + 3x - 10 = 180
7x - 10 = 180
7x = 190
x = 27.14
Now, substitute the value of x to find the angles:
Angle A = 4x = 4 * 27.14 = 108.56 degrees
Angle B = 6x + 10 = 6 * 27.14 + 10 = 166.84 degrees
Angle C = 3x - 10 = 3 * 27.14 - 10 = 71.42 degrees
Angle D = 5x = 5 * 27.14 = 135.7 degrees
Therefore, the measures of the angles in the trapezium ABCD are as follows:
Angle A = 108.56 degrees
Angle B = 166.84 degrees
Angle C = 71.42 degrees
Angle D = 135.7 degrees