The area of a kite can be found using the formula:

Area = (1/2) × d₁ × d₂

where d₁ and d₂ are the lengths of the two diagonals.

Given that the diagonals are of lengths 8 and 15, we can calculate the area as follows:

Area = (1/2) × 8 × 15
Area = 4 × 15
Area = 60

So, the area of the kite is 60. The correct answer is C) 60.

To find the radius of the circle, we first have to find the distance between the endpoints of the diameter. We can use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Given the endpoints of the diameter are (-5, 2) and (3, -4), we have:

d = √((3 - (-5))² + (-4 - 2)²)
d = √((8)² + (-6)²)
d = √(64 + 36)
d = √100 = 10

Since the distance between the endpoints of the diameter is the diameter, the radius is half of the distance:

r = d / 2
r = 10 / 2
r = 5

So, the radius of the circle is 5. The correct answer is C) 5.

In a parallelogram, adjacent angles are supplementary, which means their measures add up to 180 degrees.

If the ratio between the measures of the two adjacent angles is 4:5, we can denote the measures of the angles as 4x and 5x, respectively. Then, we know that:

4x + 5x = 180
9x = 180

Divide both sides by 9:

x = 20

Now, we can find the measure of the larger angle, 5x:

5x = 5 * 20 = 100

So, the measure of the larger angle in the parallelogram is 100 degrees. The correct answer is B) 100.

In an isosceles triangle, the base angles are equal. Given that the measures of angles B1 and B2 are each 40 degrees, we can use the fact that the sum of the measures of the interior angles of a triangle is 180 degrees:

angle_V + angle_B1 + angle_B2 = 180

Since angle_B1 = angle_B2 = 40 degrees, we have:

angle_V + 40 + 40 = 180
angle_V + 80 = 180

Subtracting 80 from both sides:

angle_V = 100

So, the measure of angle V is 100 degrees. The correct answer is D) 100.

To find the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂), we can use the formula:

(midpoint_x, midpoint_y) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Given the endpoints A(1, 6) and B(7, 4), we have:

midpoint_x = (1 + 7) / 2 = 8 / 2 = 4
midpoint_y = (6 + 4) / 2 = 10 / 2 = 5

The coordinates of the midpoint M are (4, 5). The correct answer is B) (4, 5).