The measure of an angle of a parallelogram is 12 degrees less than 3 times the measure of an adjacent angle. find the measure of all the interior angels of the parallelogram.
x=48
x=42
To find the measure of the interior angles of a parallelogram, we need to use a couple of properties of parallelograms.
First, recall that opposite angles of a parallelogram are congruent. This means that if we find the measure of one angle, we can use it to find the measures of the other three angles.
Let's call the measure of one angle x degrees. According to the problem, the measure of an adjacent angle is 3 times x degrees minus 12 degrees. So, the measure of the adjacent angle is 3x - 12 degrees.
Since opposite angles are congruent, we know that the measure of the opposite angle to x degrees is also x degrees. Similarly, the measure of the opposite angle to 3x - 12 degrees is also 3x - 12 degrees.
Now, we can set up an equation using the sum of angles in a parallelogram. The sum of the interior angles of a parallelogram is always 360 degrees.
The equation we can set up is:
x + (3x - 12) + x + (3x - 12) = 360
Simplifying the equation, we have:
8x - 24 = 360
Adding 24 to both sides of the equation, we get:
8x = 384
Dividing both sides of the equation by 8, we get:
x = 48
So, the measure of one angle is 48 degrees.
Using this value, we can find the measure of the other three angles:
- The adjacent angle is 3x - 12 = 3(48) - 12 = 144 - 12 = 132 degrees.
- The opposite angle to 48 degrees is also 48 degrees.
- The opposite angle to 132 degrees is also 132 degrees.
Therefore, the measures of all the interior angles of the parallelogram are:
48 degrees, 132 degrees, 48 degrees, and 132 degrees.
"adjacent" angles of a parallelogram add up to 180°.
so let one angle be x
then the adjacent is 3x-12
solve for x
x + 3x-12 = 180
So now you have a pair of adjacent angles, take it from there.