the measure of one interior angle of a parallelogram is 50 degrees more than 4 times the measure of another angle. find the measure of each angle.
Let's assume the measure of one angle in the parallelogram is "x" degrees.
According to the given information, the measure of another angle is 4 times this measure plus an additional 50 degrees.
So, the measure of the other angle is 4x + 50 degrees.
Since opposite angles in a parallelogram are equal, the sum of the measures of these two angles is 180 degrees.
Therefore, we can write the equation:
x + (4x + 50) = 180
Combining like terms:
5x + 50 = 180
Subtracting 50 from both sides:
5x = 130
Dividing both sides by 5:
x = 26
Therefore, one angle in the parallelogram is 26 degrees.
The measure of the other angle is 4 times this measure plus 50 degrees:
4(26) + 50 = 104 + 50 = 154 degrees.
So, the measures of the angles are 26 degrees and 154 degrees.
To solve this problem, let's denote the measure of one angle as "x" and the measure of another angle as "y".
According to the problem statement, we know that one interior angle of a parallelogram is 50 degrees more than 4 times the measure of the other angle. We can write this as an equation:
x = 4y + 50
However, we also know that the opposite interior angles of a parallelogram are congruent (equal). Therefore, we can set up another equation:
x = y
Now we have a system of equations consisting of two equations:
x = 4y + 50
x = y
To solve this system of equations, we can substitute the second equation into the first equation:
y = 4y + 50
Simplifying this equation, we have:
3y = 50
Dividing both sides of the equation by 3, we find:
y = 16.67 (rounded to two decimal places)
Now, substitute this value of y back into the second equation to find x:
x = 16.67
Therefore, the measure of each angle is approximately 16.67 degrees.
the two angles sum to 180º
x + (4x + 50) = 180