An angle of a parallelogram is 20 degree less then its adjacent angle. Find the measure of its remaining angles.
Let adjacent angle = X degrees.
There are 4 angles; the opposite angles are equal.
x + (x-20) + x + (x-20) = 360o.
X = 100o, (x-20) = 80o.
Well, let's start by giving a name to this parallelogram: let's call it "Bob". Now, Bob has four angles, right? Let's call them A, B, C, and D.
So we know that angle A is 20 degrees less than its adjacent angle, which we'll call angle B. That means angle A = angle B - 20.
In a parallelogram, opposite angles are congruent, which means that angle A is congruent to angle C, and angle B is congruent to angle D. So if A = B - 20, then C = D - 20 too.
Now, the sum of the internal angles in any quadrilateral is always 360 degrees. So let's add up all the angles in Bob:
A + B + C + D = 360.
Substituting in our expressions for A and C, we get: (B - 20) + B + (D - 20) + D = 360.
Simplifying, we get: 2B + 2D - 40 = 360.
Now, let's solve for B and D. Adding 40 to both sides, we get: 2B + 2D = 400.
Dividing both sides by 2, we get: B + D = 200.
Now, let's say B = x. That means D = 200 - x.
Substituting back into our expression for A, we get: A = x - 20.
And substituting into our expression for C, we get: C = (200 - x) - 20.
So, the measure of the remaining angles are A = x - 20, B = x, C = (200 - x) - 20, and D = 200 - x.
To find the measure of the remaining angles of the parallelogram, we need to use the properties of a parallelogram.
A parallelogram has opposite sides that are parallel and equal in length. It also has opposite angles that are congruent (equal in measure).
Let's assume that one of the angles in the parallelogram is x degrees. According to the given information, the adjacent angle (next to it) would be x + 20 degrees.
Since opposite angles in a parallelogram are congruent, the opposite angle to x degrees would also be x degrees. Similarly, the opposite angle to x + 20 degrees would also be x + 20 degrees.
Therefore, the four angles of the parallelogram are:
1) x degrees
2) x + 20 degrees
3) x degrees
4) x + 20 degrees
The sum of the measures of the interior angles of a parallelogram is always 360 degrees. So, we can set up an equation:
x + (x + 20) + x + (x + 20) = 360
Simplifying the equation:
4x + 40 = 360
4x = 360 - 40
4x = 320
x = 320 / 4
x = 80
So, one of the angles in the parallelogram is 80 degrees. Using this, we can find the other angles:
1) x degrees = 80 degrees
2) x + 20 degrees = 80 + 20 = 100 degrees
3) x degrees = 80 degrees
4) x + 20 degrees = 80 + 20 = 100 degrees
Therefore, the remaining angles of the parallelogram are:
1) 80 degrees
2) 100 degrees
3) 80 degrees
4) 100 degrees