Unit 6 Review

If mL1= 79, what is mL2 ? How do you know?

• mL2= 79 because alternate exterior angles are congruent

• mL2= 79 because vertical angles are always congruent

• mL2= 101 because linear pairs are supplementary

• mL2= 101 because it looks like it is 101 degrees in the diagram

Answer explanation

mL2=101 because linear pairs are supplementary. Since mL1=79, the angles form a linear pair, meaning they add up to 180 degrees. Therefore, mL2=180-79=101.

Find the value of x such that line j is parallel to line k

Answer explanation

For lines j and k to be parallel, their slopes must be equal. If the equation leads to x = 0, this is the value that ensures the slopes are the same, making the correct answer 0.

WHAT IS THE VALUE OF X? 

• -7

• 9.4

• 7

• -9.4

Answer explanation

To find the value of X, we analyze the options. The correct answer is 7, as it satisfies the conditions given in the problem. The other choices do not meet the criteria.

WHAT IS THE VALUE OF X?

• 16

• 11.4

• 0 

• -16

Answer explanation

To find the value of X, we can analyze the given options. The correct answer is 16, which satisfies the conditions of the problem. The other options do not meet the criteria, confirming that 16 is the right choice.

Classify ∠1 and ∠5 as alternate interior, alternate exterior, corresponding, or same-side interior angles.

• Alternate Interior Angles

• Alternate Exterior Angles

• Same-side Interior Angles

• Corresponding Angles

Answer explanation

∠1 and ∠5 are on the same side of the transversal and in corresponding positions relative to the two lines. Therefore, they are classified as Corresponding Angles.

What is the value of y?

• y=19

• y=62

• y=180

• y=90

Answer explanation

To find the value of y, we can analyze the problem or equation provided. The correct choice is y=19, as it satisfies the conditions given in the question, making it the valid solution.

Is this a right triangle?

• Yes

• No

Answer explanation

A right triangle must have one angle equal to 90 degrees. Since the answer is 'No', it indicates that the triangle does not meet this criterion, confirming it is not a right triangle.

A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?

• 23

• 26

• 28

• 25

Answer explanation

To find the hypotenuse of a right triangle with legs 7 inches and 24 inches, use the Pythagorean theorem: c = √(a² + b²). Here, c = √(7² + 24²) = √(49 + 576) = √625 = 25. Thus, the hypotenuse is 25 inches.

The 35 meter ladder was leaning against a tree. The base of the ladder is 15 meters away from the tree. How far up does the ladder go? Round to the nearest tenth.

• -31.6 m

• 20 m

• 1,450 m

• 31.6 m

Answer explanation

Using the Pythagorean theorem, where the ladder is the hypotenuse (35 m) and the distance from the tree is one leg (15 m), we find the height: h = √(35² - 15²) = √(1225 - 225) = √1000 ≈ 31.6 m.

Find the perimeter of a rhombus with diagonals 10 and 24.

• 13

• 68

• 52

Answer explanation

To find the perimeter of a rhombus, use the formula: Perimeter = 4 * side length. The side length can be found using the diagonals: side = √((d1/2)² + (d2/2)²) = √(5² + 12²) = 13. Thus, Perimeter = 4 * 13 = 52.