Final Reveiw\

Use the figure below to answer Question #1 and Question #2.

• 45°

• 50°

• 60°

• 85°

Answer explanation

In the figure, the angle marked is vertically opposite to the 50° angle, making it also 50°. Vertically opposite angles are equal.

What is the measure of ∠CGD?

• 45°

• 50°

• 60°

• 85°

Answer explanation

The measure of ∠CGD is 60° because it is an exterior angle of a triangle, and the sum of exterior angles of a triangle is always 360°.

What is the measure of ∠EGD?

• 50°

• 85°

• 90°

• 95°

Answer explanation

The measure of ∠EGD is 85° because it is an exterior angle of a triangle, and the sum of exterior angles of a triangle is always 180°.

Which equation below has no solution?

• 2(2x + 1) = 4x + 2

• 3x + 7 = x

• 3x + 6 = x + 2

• 5x + 1 = 5x - 3

Answer explanation

The equation 5x + 1 = 5x - 3 has no solution because the variables cancel out, leaving a false statement (1 = -3).

Two complementary angles are in the ratio 1:5. What is the measure of the smaller angle?

• 15°

• 30°

• 60°

• 90°

Answer explanation

Since the angles are in the ratio 1:5, the smaller angle is 1/6 of the total (1+5=6) angles. Therefore, the smaller angle is 1/6 * 90° = 15°.

Given the triangle shown below:

Answer explanation

The triangle is a right-angled triangle with one angle measuring 90 degrees. The side opposite the right angle is the hypotenuse, and the other two sides are the legs.

Given the triangle shown below:

• 50°

• 60°

• 70°

• 80°

Answer explanation

In a triangle, the sum of all angles is 180°. Since one angle is 60°, and another is 50°, the third angle must be 70° to make the total 180°. Therefore, the correct answer is 70°.

Ms. Donaldson earns $18.80 per hour for the first 40 hours she works in a week. She earned 1.5 times that amount per hour for each hour she works beyond 40 hours in a week. Last week, Ms. Donaldson worked 45.5 hours. How much money did she earn?

• A) $846.50

• B) $900.00

• C) $940.50

• D) $980.00

Answer explanation

Ms. Donaldson earned $18.80 per hour for the first 40 hours and 1.5 times that amount for the extra 5.5 hours. Calculating total earnings: (40 * $18.80) + (5.5 * $18.80 * 1.5) = $846.50. Therefore, the correct answer is A) $846.50.

Simplify the following expression: 9 - 2(x - 3)

• A) 9 - 2x + 6

• B) 9 - 2x - 6

• C) 9 + 2x - 6

• D) 9 + 2x + 6

Answer explanation

To simplify the expression, distribute the -2: 9 - 2x + 6. Therefore, the correct choice is A) 9 - 2x + 6.

A guy wire is attached to the top of a radio tower to help support it. The tower is 72 feet tall and the wire is attached to the ground 50 feet from the midline of the tower. Find the length of the guy wire to the nearest foot.

• A) 88 feet

• B) 90 feet

• C) 85 feet

• D) 80 feet

Answer explanation

To find the length of the guy wire, use the Pythagorean theorem: 72^2 + 50^2 = c^2. Calculate c ≈ 88 feet, so the correct answer is A) 88 feet.