Find each angle of a parallelogram if its two consecutive angles are in the ratio of 1 : 3.
To find each angle of a parallelogram, we need to know the relationship between the consecutive angles. Given that the two consecutive angles are in the ratio of 1:3, let's assume the measure of the first angle is x degrees.
According to the given ratio, the measure of the second consecutive angle would be 3x degrees.
In a parallelogram, the opposite angles are equal. So, the measure of the third angle would also be 3x degrees.
Now, let's find the measure of the fourth and final angle of the parallelogram.
The sum of all angles in a parallelogram is 360 degrees. Therefore,
x + 3x + 3x + Fourth angle = 360 degrees
7x + fourth angle = 360 degrees
Now, we can isolate the fourth angle:
Fourth angle = 360 degrees - 7x
So, each angle of the parallelogram can be expressed as follows:
First angle = x degrees
Second angle = 3x degrees
Third angle = 3x degrees
Fourth angle = 360 degrees - 7x
By substituting any value of x, we can find the respective measures of all four angles of the parallelogram.
remember, consecutive angles in a parallelogram have to be supplementary, that is, they add up to 180°
let the angles be x and 3x
x + 3x = 180
continue ....