The sum of two opposite angles of a parallelogram is 130 degree. Find the measure of each of its angle.
Opposite angles of a parallelogram are equal. The sum of adjacent angles is 180°.
Thus one of the two opposite angles is 130/2=65°. The adjacent (obtuse) angle is 180-65=?°
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To find the measure of each angle in a parallelogram, we need to know that opposite angles in a parallelogram are congruent, meaning they have the same measure. Let's assume that the two opposite angles are x and y degrees.
Given that the sum of the two opposite angles is 130 degrees, we can write the equation:
x + y = 130
Since opposite angles in a parallelogram are congruent, we can also write another equation:
x = y
Now we have a system of equations:
x + y = 130
x = y
To solve this system of equations, we can substitute the second equation into the first equation:
x + x = 130
Combining like terms, we get:
2x = 130
To isolate x, we divide both sides of the equation by 2:
x = 130/2
x = 65
Now, substitute the value of x back into the second equation to find y:
65 = y
So, the measure of each angle in the parallelogram is 65 degrees.