All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
3161
A polygon has 20 diagonals. How many sides does it have?
Answer:
8
The formula for the number of diagonals is n(n - 3) / 2 = 20. Multiplying by 2 gives n(n - 3) = 40. The factors of 40 that differ by 3 are 8 and 5 (so n=8 and n-3=5). Thus, the polygon has 8 sides (an octagon).
3162
What is the measure of each exterior angle of a regular hexagon?
Answer:
60 degrees
The sum of the exterior angles of any polygon is 360 degrees. A regular hexagon has 6 equal exterior angles. Each exterior angle = 360 / 6 = 60 degrees.
3163
The sum of the interior angles of a polygon is 1260 degrees. How many sides does it have?
Answer:
9
Using the formula for the sum of interior angles: (n - 2) * 180 = 1260. Dividing by 180 gives (n - 2) = 7. Adding 2 gives n = 9. The polygon is a nonagon (9 sides).
3164
If the exterior angle of a regular polygon is 40 degrees, how many sides does the polygon have?
Answer:
9
The sum of the exterior angles of any convex polygon is 360 degrees. For a regular polygon, all exterior angles are equal. Number of sides = 360 / (exterior angle measure) = 360 / 40 = 9 sides.
3165
What is the measure of each interior angle in a regular octagon?
Answer:
135 degrees
First, find the sum of the interior angles of an octagon (n = 8): (8 - 2) * 180 = 6 * 180 = 1080 degrees. Since it is regular, all 8 angles are equal. Each interior angle = 1080 / 8 = 135 degrees.
3166
How many diagonals does a regular hexagon have?
Answer:
9
The number of diagonals in a polygon with n sides is given by the formula n(n - 3) / 2. For a hexagon, n = 6. Number of diagonals = 6(6 - 3) / 2 = 6(3) / 2 = 18 / 2 = 9.
3167
What is the sum of the interior angles of a pentagon?
Answer:
540 degrees
The formula for the sum of interior angles of an n-sided polygon is (n - 2) * 180 degrees. For a pentagon, n = 5. So, Sum = (5 - 2) * 180 = 3 * 180 = 540 degrees.
3168
The area of a parallelogram is 64 cm². If the base is 4 times its height, what is the height?
Answer:
4 cm
Let the height be h. Then the base is 4h. Area = base * height = (4h) * h = 4h². Given Area = 64, so 4h² = 64, meaning h² = 16. Therefore, the height h = 4 cm.
3169
What is the side length of a rhombus if its diagonals are 10 cm and 24 cm?
Answer:
13 cm
The diagonals of a rhombus bisect each other at right angles (90 degrees). This forms four right-angled triangles. The legs of each triangle are half the diagonals: 5 cm and 12 cm. The side of the rhombus is the hypotenuse: √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
3170
What is the perimeter of a kite if its two distinct adjacent side lengths are 8 cm and 12 cm?
Answer:
40 cm
A kite has two pairs of equal-length adjacent sides. Thus, the perimeter is the sum of all four sides: 2 * (side1) + 2 * (side2). Perimeter = 2(8) + 2(12) = 16 + 24 = 40 cm.