#1
What is the sum of interior angles of a triangle?
180 degrees
ExplanationAngles in a triangle add up to 180 degrees.
#2
What is the formula to find the area of a circle?
πr^2
ExplanationArea of a circle is π times the square of its radius.
#3
What is the formula for finding the circumference of a circle?
2πr
ExplanationCircumference of a circle is 2π times its radius.
#4
What does the term 'hypotenuse' refer to in a right triangle?
The longest side, opposite the right angle
ExplanationHypotenuse is the longest side across the right angle in a triangle.
#5
What is the formula to find the perimeter of a rectangle?
2 * length + 2 * width
ExplanationPerimeter of a rectangle is twice its length plus twice its width.
#6
What is the Pythagorean theorem used for?
Determining the lengths of the sides of a right triangle
ExplanationPythagorean theorem calculates side lengths in a right triangle.
#7
What is the sum of the exterior angles of any polygon?
360 degrees
ExplanationSum of exterior angles of a polygon is always 360 degrees.
#8
What is the measure of each interior angle in a regular hexagon?
120 degrees
ExplanationEach interior angle in a regular hexagon measures 120 degrees.
#9
What is the formula to find the volume of a sphere?
(4/3)πr^3
ExplanationVolume of a sphere is (4/3)π times the cube of its radius.
#10
In a right triangle, what is the relationship between the squares of the lengths of the two shorter sides and the square of the length of the hypotenuse?
The sum of the squares of the two shorter sides equals the square of the hypotenuse
ExplanationPythagorean theorem: a^2 + b^2 = c^2.
#11
What is the equation of a line in slope-intercept form?
y = mx + b
ExplanationSlope-intercept form of a line equation is y = mx + b.
#12
What is the midpoint formula for a line segment with endpoints (x1, y1) and (x2, y2)?
((x1 + x2)/2, (y1 + y2)/2)
ExplanationMidpoint formula: Average of x-coordinates and y-coordinates of endpoints.
#13
What is the measure of each interior angle in a regular pentagon?
108 degrees
ExplanationEach interior angle in a regular pentagon measures 108 degrees.
#14
In a circle, what is the relationship between the radius and the diameter?
The radius is half the diameter
ExplanationRadius is half the diameter of a circle.
#15
What is the formula to find the area of a circle sector?
(θ/360) * πr^2
ExplanationArea of a circle sector: Fraction of circle area based on angle.