If an angle of a Parallelogram is Two-Third of its adjacent angle, then the Smallest angle of the Parallelogram is

If an angle of a Parallelogram is Two-Third of its adjacent angle, then the Smallest angle of the Parallelogram is

A parallelogram has some unique properties that help us determine unknown angles when the required data is provided. A parallelogram has two pairs of opposite angles that are equal. Adjacent angles in a parallelogram are supplementary, which means they add up to 180 degrees.

In this problem, we are given that one angle of the parallelogram is two-thirds of its adjacent angle.

Let's denote one angle of the parallelogram as y degrees.

Therefore, the adjacent angle is 2/3 x y degrees

Since adjacent angles are supplementary, we can set up the equation

y + 2/3 x y = 180°

5/3 x y = 180°

Therefore y = 180° x 3/5 = 108°

The adjacent angle, being two-thirds of y, is

2/3 x 108° = 72°

Hence, the smallest angle in the parallelogram is 72°

Concept of Parallelogram

A parallelogram is a four-sided figure with opposite sides that are parallel and equal in length. It has some interesting properties related to its angles.

Opposite Angles:

The opposite angles in a parallelogram are equal. This means that if one angle is known, the angle directly across from it will be the same.

Adjacent Angles:

Adjacent angles in a parallelogram are supplementary. This means that any two angles next to each other add up to 180 degrees.

Special Angle Relationships

If the measure of one angle is given as a fraction of its adjacent angle, specific calculations can determine the actual angles. For instance, if one angle is given as two-thirds of its adjacent angle, we can set up an equation to find the measures of these angles.

Calculating Angles

• If one angle is x and its adjacent angle is related to x, their sum is 180 degrees.
• Combine the terms to isolate x and solve for it. This will give the measure of one angle.
• Multiply the found angle by the given fraction to find the adjacent angle.