Using the conditional statement below, match the correct statement to the inverse, converse, contrapositive and biconditional statement If two angles form a linear pair, then they are supplementary. (4 points) If two angles are supplementary, then they form a linear pair If two angles are not supplementary, then they do not form a linear pair Two angles form a linear pair if and only if they are supplementary If two angles do not form a linear pair, then they are not supplementary. (Contrapositive)(Biconditional)(Inverse)(Converse)

Answer 1

Inverse: If two angles are not supplementary, then they do not form a linear pair.
Converse: If two angles are supplementary, then they form a linear pair.
Contrapositive: If two angles do not form a linear pair, then they are not supplementary.
Biconditional: Two angles form a linear pair if and only if they are supplementary.

Answer 2

SX¯¯¯¯¯¯¯¯ bisects <RST. m<RST = 10x. m<XST = 3x+16. Find m<RSX(2 points) m<RSX = degrees (Type the number ONLY)

Answer 3

To find the measure of ∠RSX, we need to use the angle bisector theorem. According to the theorem, the measure of ∠RST divided by the measure of ∠XST is equal to the measure of ∠RSX divided by the measure of ∠XSR.

So, we have:

m<RST / m<XST = m<RSX / m<XSR

Substituting the given values:

10x / (3x + 16) = m<RSX / m<XSR

To find m<RSX, we'll solve for x first. Cross-multiply the equation:

10x * m<XSR = (3x + 16) * m<RSX

10xm<XSR = 3xm<RSX + 16m<RSX

Rearrange the equation:

10xm<XSR - 3xm<RSX = 16m<RSX

Factor out x:

x(10m<XSR - 3m<RSX) = 16m<RSX

Solve for x:

x = (16m<RSX) / (10m<XSR - 3m<RSX)

Since we only want to find m<RSX, we can assume values for m<XSR and m<RST. Let's say m<XSR = 40 and m<RST = 100. Plugging these values into the equation, we have:

x = (16m<RSX) / (10(40) - 3(100))

x = (16m<RSX) / (400 - 300)

x = (16m<RSX) / 100

Multiplying both sides by 100:

100x = 16m<RSX

Dividing both sides by 16:

6.25x = m<RSX

Since x represents the whole number of degrees in ∠RST, we'll choose a value that makes x a whole number. Let's say x = 8.5.

Substituting x = 8.5:

m<RSX = 6.25(8.5)

m<RSX = 53.125

Therefore, m<RSX is approximately 53.125 degrees.

Answer 4

Which of the following is a correct conditional statement(1 point) Responses All rectangles are parallelograms All rectangles are parallelograms If a shape is a parallelogram, then it is a rectangle If a shape is a parallelogram, then it is a rectangle If a shape is a rectangle, then it is a parallelogram If a shape is a rectangle, then it is a parallelogram A rectangle can be a parallelogram A rectangle can be a parallelogram

Answer 5

The correct conditional statement is:

If a shape is a rectangle, then it is a parallelogram.

Answer 6

The measure of two verticle angles are 9x + 3 and 12x - 6. Find x.(1 point) Responses 9.5 9.5 8.7 8.7 12 12 3 3

Answer 7

To find x, we set the two vertical angles equal to each other and solve for x:

9x + 3 = 12x - 6

To isolate x, we subtract 9x from both sides:

3 = 3x - 6

Next, we add 6 to both sides:

9 = 3x

Dividing both sides by 3:

3 = x

So, x = 3.

Answer 8

What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 3 is also divisible by 6. (1 point) Responses 30 30 12 12 26 26 9

Answer 9

A counterexample for the conjecture that any number divisible by 3 is also divisible by 6 is the number 9.

9 is divisible by 3, but it is not divisible by 6, as 9 divided by 6 equals 1 remainder 3.