The sum of two opposite angles of a parallelogram is 140 degree. Find all the angles of the parallelogram.
so, each one is 70°
Now you just need to recall that consecutive angles are supplementary.
Thus, the other two angles are 110°
To find the angles of a parallelogram, we can use the fact that opposite angles are congruent.
Let's assume one of the angles is x. Since the sum of two opposite angles is 140 degrees, the other opposite angle is also 140 degrees.
So we have the following angles in the parallelogram:
1) Angle 1 = x
2) Angle 2 = 140 degrees
3) Angle 3 = x
4) Angle 4 = 140 degrees
Since the opposite angles are congruent, we can set up the following equation:
Angle 1 + Angle 3 = 180 degrees (since the sum of adjacent angles in a parallelogram is 180 degrees)
x + x = 180 degrees
2x = 180 degrees
x = 90 degrees
Therefore, the four angles of the parallelogram are:
1) Angle 1 = 90 degrees
2) Angle 2 = 140 degrees
3) Angle 3 = 90 degrees
4) Angle 4 = 140 degrees
To solve this problem, let's start by understanding the properties of a parallelogram. In a parallelogram, opposite angles are congruent, which means they have the same measure.
Let's assume the angles of the parallelogram are A, B, C, and D. According to the problem, the sum of two opposite angles is 140 degrees. Without loss of generality, let's assume that A and C are the opposite angles with a sum of 140 degrees.
So, we have the equation A + C = 140.
Since opposite angles in a parallelogram are congruent, we can also say that B and D are opposite angles and have the same measure as A and C.
Now, we have two equations:
A + C = 140
B = A
D = C
We can use these equations to find all the angles of the parallelogram.
Since B = A, we can substitute B for A in the first equation:
B + C = 140
Now, using the third equation, we can substitute C for D in the second equation:
B + D = 140
Since D = C, we can rewrite this equation as:
B + C = 140
We now have two equations that are identical:
B + C = 140
This means that the values of B and C can be any two numbers that add up to 140 degrees. Since we don't have any other information about the angles, we cannot determine their specific measures.
Therefore, the angles of the parallelogram are not uniquely determined based on the given information.