Geometry Concepts and Problem Solving

This video tutorial covers a range of geometry problems, including complementary and supplementary angles, midpoint and segment length calculations, triangle angle ratios, circle geometry, and polygon angles. It provides step-by-step solutions and explanations for each problem, helping students understand key concepts and improve their problem-solving skills in geometry.

If angles ABD and CBD are complementary and their measures are 5x + 18 and 7x respectively, what is the measure of angle ABD?

• 42 degrees

• 60 degrees

• 48 degrees

• 54 degrees

In a triangle with angles in the ratio 5:7:8, what is the difference between the largest and smallest angle?

• 27 degrees

• 45 degrees

• 36 degrees

• 18 degrees

How many diagonals does a regular hexagon have?

• 6

• 7

• 8

• 9

What is the area of a rhombus if one diagonal is 12 and the other is 16?

• 72 square units

• 96 square units

• 108 square units

• 120 square units

What is the volume of a rectangular prism with dimensions 12, 5, and 4?

• 240 cubic units

• 300 cubic units

• 280 cubic units

• 260 cubic units

What is the diagonal length of a rectangular prism with dimensions l = 12, w = 5, and h = 4?

• 13.6

• 14.4

• 15.2

• 12.8

In similar triangles, if the long side of the first triangle is 12 and the short side is 8, what is the long side of the second triangle if its short side is 20?

• 25

• 40

• 30

• 35

If B is the midpoint of AC and D is the midpoint of CE, and BD is 4x - 8, what is the length of BD when AE is 5x - 1?

• 10

• 12

• 14

• 16

What is the slope of a line perpendicular to a line with a slope of 3?

• -3

• 3

• -1/3

• 1/3

How do you calculate the area of a regular hexagon with a side length of 20?

• 500√3

• 600√3

• 700√3

• 400√3