Int. Math 2 - Study Quiz For Test 10.1 - 10.4

Explanation
The given sentence states that the measure of the angle is 81 degrees more than twice that of its supplement. To find the measures of the two angles, we can represent the measure of the angle as x and the measure of its supplement as 2x + 81. Since the sum of an angle and its supplement is always 180 degrees, the equation that represents this relationship is x + (2x + 81) = 180.

Explanation
The correct answer is angles B, C and A, D. Alternate exterior angles are formed when a transversal intersects two parallel lines. In this case, angles B and C are alternate exterior angles because they are on opposite sides of the transversal and outside the parallel lines. Similarly, angles A and D are also alternate exterior angles because they are on opposite sides of the transversal and outside the parallel lines.

Explanation
Complementary angles are defined as two angles that add up to 90 degrees. They do not always have the same measure, as the measure of one angle can be larger or smaller than the other as long as their sum is 90 degrees. Therefore, the statement "Complementary angles always have the same measure" is not true.

Explanation
The sum of the measures of the three angles of any triangle is always 180 degrees. This is a fundamental property of triangles and is true for all types of triangles, whether they are equilateral, isosceles, or scalene. The sum of the angles in a triangle is independent of the lengths of the sides or the type of triangle. This property can be proven using geometric principles and is a basic concept in geometry.

Explanation
Using similar triangles, we can determine the height of the tree. By comparing the height of the tree to the height of the figure, we can set up a proportion. Since the figure is 6m tall and the tree is unknown, we can set up the proportion as 6m/10m = x/20m. Solving for x, we find that the height of the tree is 20m.

Explanation
The distance from home plate to second base on a baseball diamond is 127.3 ft. This is because a baseball diamond is a square with 90-foot sides, and the distance from one corner of a square to the opposite corner is found by multiplying the length of one side by the square root of 2. In this case, 90 ft multiplied by the square root of 2 is approximately equal to 127.3 ft.

Explanation
To find the cost of fencing, we need to calculate the perimeter of the playground. The perimeter of a rectangle is calculated by adding all four sides. In this case, the length of the rectangle is 400 feet and the width is 200 feet. So, the perimeter is (2 * 400) + (2 * 200) = 800 + 400 = 1200 feet. Since fencing costs $14 per yard, we need to convert the feet to yards by dividing 1200 by 3, which equals 400 yards. Finally, we multiply the cost per yard ($14) by the number of yards (400) to get the total cost, which is $5600.

Explanation
The sum of the measures of the angles of a polygon with n sides is given by the formula 180(n - 2). This formula is derived from the fact that the sum of the interior angles of a polygon is always equal to (n - 2) times 180 degrees. Therefore, the correct answer is 180(n - 2).

Explanation
To find the cost of carpeting the rectangular floor, we need to calculate the area of the floor first. The area of a rectangle is found by multiplying its length by its width. In this case, the length is 9 feet and the width is 21 feet. Multiplying 9 by 21 gives us 189 square feet. Since the carpet is priced per square yard, we need to convert the area to square yards. There are 9 square feet in 1 square yard, so dividing 189 by 9 gives us 21 square yards. Finally, we multiply the area in square yards (21) by the cost per square yard ($26.50) to get the total cost, which is $556.50.

Explanation
To find the cost of plastering, we need to calculate the area of the wall. The wall is 60 feet long and 9 feet high, so the total area is 60 feet * 9 feet = 540 square feet. Since there are 9 square feet in a square yard, the area in square yards is 540 square feet / 9 = 60 square yards. The plastering contractor charges $18 per square yard, so the total cost of plastering is 60 square yards * $18 = $1080. Therefore, the correct answer is $1080.