Math Quiz: Geometry Exam!

Explanation
All angles in a triangle add up to 180 degrees.

Explanation
The Pythagorean theorem states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, the correct answer is "Right angled triangle" because the Pythagorean theorem only applies to this specific type of triangle.

Explanation
A sphere is a three-dimensional shape that is perfectly round in shape, resembling a ball. It is a geometric figure where all points on its surface are equidistant from the center point. The options "Circle" and "Ball" are not accurate descriptions for this shape, as a circle refers to a two-dimensional shape and a ball is a more general term that can refer to objects of various shapes. Therefore, the correct answer for this question is "Sphere."

Explanation
An obtuse angle is the largest angle out of the three options given. It measures more than 90 degrees but less than 180 degrees. A right angle measures exactly 90 degrees, while an acute angle measures less than 90 degrees. Therefore, the biggest angle is an obtuse angle.

Explanation
A polygon is defined as a closed figure with straight lines. Since the given figure is closed and all of its sides are straight lines, it meets the criteria of being a polygon. Therefore, the correct answer is "Yes".

Explanation
The given statement is true. The formula for finding the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius of the circle. This formula is derived from the definition of the circumference, which is the distance around the circle. By multiplying the radius by 2π, we obtain the length of the circumference. Therefore, the statement is correct.

Explanation
The ratio of the measures of the angles in a triangle is given as 3:6:1. To find the measure of each angle, we need to divide the total sum of the angles in a triangle, which is 180 degrees, according to the given ratio.

The first angle can be found by multiplying 3 by the ratio factor, giving us 3 * (180/10) = 54 degrees.

The second angle can be found by multiplying 6 by the ratio factor, giving us 6 * (180/10) = 108 degrees.

The third angle can be found by multiplying 1 by the ratio factor, giving us 1 * (180/10) = 18 degrees.

Therefore, the measure of each angle in the triangle is 54, 108, and 18 degrees.

Explanation
In a triangle, the ratio of the measures of the shortest sides to the perimeter is given as 3:7:5. This means that the shortest side is 3 units, the second shortest side is 7 units, and the longest side is 5 units. The perimeter of the triangle is given as P = 150. To find the measure of the shortest side, we can set up the equation 3x + 7x + 5x = 150, where x is the common ratio. Simplifying this equation, we get 15x = 150, which gives us x = 10. Therefore, the measure of the shortest side is 3x = 3 * 10 = 30.

Explanation
The given proportion can be solved by cross-multiplying. Since x is equal to 3 in the first equation and x is equal to 9 in the second equation, we can set up the proportion as 3/9 = 12/O. By cross-multiplying, we get 3O = 9 * 12, which simplifies to 3O = 108. Dividing both sides by 3, we find that O is equal to 36. Therefore, the correct answer is x = 9.

Explanation
The triangles shown are similar because the scale factor between corresponding sides is 3/4. This means that each side of the smaller triangle is 3/4 the length of the corresponding side in the larger triangle.

Explanation
The given answer x=5 is correct because it is one of the values provided in the question. The question asks to find the value of x, and among the options given, x=5 is one of them. Therefore, x=5 is the correct answer.