Question

If an angle of a parallelogram is one third of its adjacent angle, find the smallest size?

Answer 1

The smallest angle in the parallelogram is 45 degrees. This is found by setting up an equation based on the relationships between the angles in a parallelogram.

Let's denote the measure of one angle in the parallelogram as x. According to the given information, the adjacent angle measures 3x. In a parallelogram, opposite angles are equal, so the opposite angle to x also measures x. Similarly, the opposite angle to 3x measures 3x.

Since the sum of interior angles in a quadrilateral is 360 degrees, we can set up an equation:

x + 3x + x + 3x = 360

Combine like terms:

8x = 360

Now, solve for x:

`\[ x = (360)/(8) = 45 \]`

Therefore, the smallest angle in the parallelogram is x = 45 degrees.