Quadrilaterals and Polygons - Exam Prep for Students

Quadrilaterals and Polygons - Problems on Circles

Q. If a circle is inscribed in a quadrilateral, what is the relationship between the lengths of the sides?

Solution

For a quadrilateral to have an inscribed circle, the sum of the lengths of opposite sides must be equal.

Correct Answer: B — Sum of opposite sides is equal

Q. If a regular hexagon has a side length of 3 cm, what is the perimeter of the hexagon?

Solution

The perimeter of a regular hexagon is calculated as 6 times the side length. Therefore, perimeter = 6 × 3 cm = 18 cm.

Correct Answer: D — 18 cm

Q. If a regular hexagon has a side length of 6 cm, what is the perimeter of the hexagon?

Solution

The perimeter of a regular hexagon is calculated as 6 times the side length. Therefore, perimeter = 6 × 6 cm = 36 cm.

Correct Answer: C — 36 cm

Q. If the radius of a circle is 7 cm, what is the circumference of the circle?

Solution

The circumference of a circle is calculated using the formula 2πr. Therefore, circumference = 2π × 7 cm = 14π cm.

Correct Answer: B — 21π cm

Q. If the radius of a circle is 7 cm, what is the circumference?

Solution

The circumference of a circle is calculated using the formula 2πr. Thus, the circumference is 2π × 7 cm = 14π cm.

Correct Answer: B — 21π cm

Q. In a cyclic quadrilateral, what is the relationship between the opposite angles?

Solution

In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.

Correct Answer: B — They are supplementary

Q. In a parallelogram, if one angle measures 70 degrees, what is the measure of the opposite angle?

Solution

In a parallelogram, opposite angles are equal. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees.

Correct Answer: A — 70 degrees

Q. In a triangle, if two angles measure 45 degrees and 55 degrees, what is the measure of the third angle?

Solution

The sum of the angles in a triangle is always 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 80 degrees.

Correct Answer: B — 90 degrees

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