Measure of ∠BDC in Trapezoid ABCD

In the figure below, lines m and n are parallel, transversals r and s intersect to form an angle of measure x°, and 2 other angle measures are as marked. What is the value of x?

• 15

• 25

• 35

• 65

• 80

In the figure below, ABCD is a trapezoid, E lies on AD, and angle measures are as marked. What is the measure of ∠BDC?

• 15°

• 25°

• 30°

• 35°

• 45°

A triangle with a perimeter of 66 inches has one side that is 16 inches long. The lengths of the other two sides have a ratio of 2:3. What is the length, in inches, of the longest side of the triangle?

• A. 16

• B. 20

• C. 30

• D. 40

• E. 50

In the figure below, B is on AC, E is on DF, AC is parallel to DF, and BE is congruent to BF. What is the measure of ∠DEB?

• 35°

• 135°

• 145°

• 155°

• 215°

In ΔABC below, D, E, and F are points on AB, BC, and AC, respectively, and DF is congruent to EF. What is the sum of the measures of the angles marked x and y?

• 40°

• 80°

• 90°

• 100°

• 130°

Which of the following lists gives 2 of the 3 interior angle measurements of a triangle for which the third angle measurement would be equal to 1 of the 2 given measurements?

• 20°, 40°

• 30°, 60°

• 40°, 100°

• 45°, 120°

• 50°, 60°

A ladder is 10 ft long and reaches 8 ft up a wall, as shown below. How many feet is the bottom of the ladder from the base of the wall?

• 2

• 3

• 6

• √2

• √164

The ratio of the side lengths for a triangle is exactly 12:14:15. In a second triangle similar to the first, the shortest side is 8 inches long. To the nearest tenth of an inch, what is the length of the longest side of the second triangle?

• 11.0

• 10.0

• 9.3

• 6.4

• Cannot be determined from the given information.

Members of the fire department lean a 30-foot ladder against a building. The side of the building is perpendicular to the level ground so that the base of the ladder is 10 feet away from the base of the building. To the nearest foot, how far up the building does the ladder reach?

• 10

• 20

• 28

• 31

• 40

Which of the following sets of 3 numbers could be the side lengths, in meters, of a 30°-60°-90° triangle?

• 1, 1, 1

• 1, 1, √2

• 1, √2, √2

• 1, √2, √3