Parallelogram Angle Properties

In a parallelogram, adjacent angles are supplementary (add up to 180 degrees), and opposite angles are equal.

Setting Up the Equation

Let the smallest angle of the parallelogram be represented by x.

According to the question, one angle is $48^\circ$ less than twice the smallest angle. This angle can be written as $2x - 48^\circ$.

Since these two angles are adjacent in a parallelogram, their sum must be $180^\circ$.

Therefore, the equation is:

$x + (2x - 48^\circ) = 180^\circ$

Solving for the Smallest Angle

1. Combine like terms: $3x - 48^\circ = 180^\circ$
2. Add $48^\circ$ to both sides: $3x = 180^\circ + 48^\circ$
3. Simplify: $3x = 228^\circ$
4. Divide by 3: $x = \frac{228^\circ}{3}$
5. Calculate the value of x: $x = 76^\circ$

So, the smallest angle is $76^\circ$.

Finding the Largest Angle

The angles in the parallelogram are $x$ and $2x - 48^\circ$. We found $x = 76^\circ$.

Calculate the other angle:

$2x - 48^\circ = 2(76^\circ) - 48^\circ$

$= 152^\circ - 48^\circ$

$= 104^\circ$

The two distinct angles in the parallelogram are $76^\circ$ and $104^\circ$. The largest angle is $104^\circ$.