Maths Geometry

1. In a parallelogram, which statement is true regarding the opposite side and opposite angles?

The opposite side and opposite angles of a parallelogram are perpendicular.

The opposite side and opposite angles of a parallelogram are always congruent.

The opposite side and opposite angles of a parallelogram are parallel.

Cosider triangle ABC and CDA

In a parallelogram, the opposite sides are equal in length and the opposite angles are also equal in measure. This is a fundamental property of parallelograms that can be proven by considering the triangles formed within the parallelogram.

Explanation

In a parallelogram, the opposite sides are equal in length and the opposite angles are also equal in measure. This is a fundamental property of parallelograms that can be proven by considering the triangles formed within the parallelogram.

2. What is the measure of the interior angle of a 12-sided figure?

120 degrees

135 degrees

150 degree

160 degrees

To find the measure of the interior angle of a regular polygon, you can use the formula: interior angle = (n-2) * 180 / n, where n is the number of sides. In this case, for a 12-sided figure, the interior angle would be (12-2) * 180 / 12 = 150 degrees.

Explanation

To find the measure of the interior angle of a regular polygon, you can use the formula: interior angle = (n-2) * 180 / n, where n is the number of sides. In this case, for a 12-sided figure, the interior angle would be (12-2) * 180 / 12 = 150 degrees.

3. Can a regular polygon exist?

I'm not sure

No

Maybe

Yes

A regular polygon is a polygon with all sides and angles being equal. Therefore, a regular polygon can indeed exist.

Explanation

A regular polygon is a polygon with all sides and angles being equal. Therefore, a regular polygon can indeed exist.

4. Two adjacent angles of a parallelogram are equal. What is the measure of each?

45 degrees

60 degrees

120 degrees

90 degree

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Therefore, if two adjacent angles are equal, they must each measure 90 degrees.

Explanation

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Therefore, if two adjacent angles are equal, they must each measure 90 degrees.