the measure of an angle of a parallelogram is 12 degrees less than 3 times the measure of an adjacent angle. explain how to find the measures of all the interior angles of the parallelogram.
well, you know that in a ||gram, the adjacent angles must add up to 180°
let one angle be Ø,
the other is 3Ø-12
solve Ø + 3Ø-12 = 180
etc
To find the measures of all the interior angles of a parallelogram, we need to use the given information. Remember that the opposite angles of a parallelogram are congruent, and the adjacent angles are supplementary (they add up to 180 degrees).
Let's break down the problem step by step:
1. Let's assume the measure of one of the adjacent angles is x degrees.
- This means the measure of the other adjacent angle is also x degrees (since opposite angles are congruent).
2. The problem states that one of the angles is 12 degrees less than 3 times the measure of an adjacent angle.
- So, one angle measures (3x - 12) degrees.
3. Since the adjacent angles are supplementary (meaning they add up to 180 degrees), the equation can be set up as follows:
x + (3x - 12) = 180
4. Solve the equation by simplifying and combining like terms:
4x - 12 = 180
4x = 192
x = 48
5. Now that we have found the measure of one adjacent angle (x = 48 degrees), we can find the measure of the other adjacent angle:
The other adjacent angle is also 48 degrees.
6. Finally, to find the measures of all the interior angles:
- The measure of the angle that is 12 degrees less than 3 times the measure of an adjacent angle is (3x - 12) = (3 * 48 - 12) = 132 degrees.
- Since opposite angles are congruent, the other opposite angle also measures 132 degrees.
So, the measures of all the interior angles in the parallelogram are:
- Two adjacent angles: 48 degrees each.
- Two opposite angles: 132 degrees each.