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)
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.
SX¯¯¯¯¯¯¯¯ bisects <RST. m<RST = 10x. m<XST = 3x+16. Find m<RSX(2 points) m<RSX = degrees (Type the number ONLY)
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.
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
The correct conditional statement is:
If a shape is a rectangle, then it is a parallelogram.
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
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.
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
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.
To determine the inverse, converse, contrapositive, and biconditional statement of the given conditional statement, it's important to understand each of these types of statements.
1. Inverse: To form the inverse of a conditional statement "If p, then q," we negate both the hypothesis (p) and the conclusion (q). It becomes "If not p, then not q."
2. Converse: The converse of a conditional statement "If p, then q," involves switching the hypothesis and the conclusion. It becomes "If q, then p."
3. Contrapositive: To form the contrapositive of a conditional statement "If p, then q," we both negate and switch the hypothesis and conclusion. It becomes "If not q, then not p."
4. Biconditional: A biconditional statement combines a conditional statement and its converse. It states that two statements are both true or both false. It can be expressed as "p if and only if q" or "p ⟺ q".
Now let's apply these definitions to the given conditional statement:
"If two angles form a linear pair, then they are supplementary."
Inverse: "If two angles do not form a linear pair, then they are not supplementary."
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."
Therefore, the answers are as follows:
Inverse: If two angles do not form a linear pair, then they are not supplementary.
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.