in parallelogram pqrs, if angle p = 70°, what is the measure of angle r?
a. 70°
b. 110°
c. 120°
d. 90°

in a parallelogram, which of the following relationships is always true?
a. the diagonals are congruent
b. all angles are equal
c. the sum of the measures of any two consecutive angles is 180°
d. opposite angles are supplementary

in rectangle hijk, hi = 4y + 6 and jk = 5y - 9. if opposite sides are congruent, what is the value of y?
a. 15
b. 9
c. 12
d. 6

in a parallelogram, the measure of two consecutive angles are 3x + 10° and 2x + 5°. what is the value of x?
a. x = 30
b. x = 25
c. x = 33
d. x = 20

an interior designer is creating a quadrilateral coffee - table with vertices at a(0,0), b(0,2), c(8, - 2), and d(2, - 4). which property can prove that the table is a parallelogram?
a. opposite sides are congruent
b. diagonals are congruent
c. all angles are right angles
d. opposite sides are perpendicular

in parallelogram pqrs, if diagonal pr is bisected at point o and po = 3x + 4 while or = 5x - 2, what is the value of x?
a. 1
b. 4
c. 2
d. 3

Question

in parallelogram pqrs, if angle p = 70°, what is the measure of angle r?
 a. 70°
 b. 110°
 c. 120°
 d. 90°

in a parallelogram, which of the following relationships is always true?
 a. the diagonals are congruent
 b. all angles are equal
 c. the sum of the measures of any two consecutive angles is 180°
 d. opposite angles are supplementary

in rectangle hijk, hi = 4y + 6 and jk = 5y - 9. if opposite sides are congruent, what is the value of y?
 a. 15
 b. 9
 c. 12
 d. 6

in a parallelogram, the measure of two consecutive angles are 3x + 10° and 2x + 5°. what is the value of x?
 a. x = 30
 b. x = 25
 c. x = 33
 d. x = 20

an interior designer is creating a quadrilateral coffee - table with vertices at a(0,0), b(0,2), c(8, - 2), and d(2, - 4). which property can prove that the table is a parallelogram?
 a. opposite sides are congruent
 b. diagonals are congruent
 c. all angles are right angles
 d. opposite sides are perpendicular

in parallelogram pqrs, if diagonal pr is bisected at point o and po = 3x + 4 while or = 5x - 2, what is the value of x?
 a. 1
 b. 4
 c. 2
 d. 3

Accepted Answer

### 1. In parallelogram $PQRS$, if angle $P = 70^{\circ}$, what is the measure of angle $R$?
# Explanation:
## Step1: Recall parallelogram property
In a parallelogram, opposite - angles are equal.
## Step2: Identify opposite angles
Angle $P$ and angle $R$ are opposite angles in parallelogram $PQRS$.
# Answer:
A. $70^{\circ}$

### 2. In a parallelogram, which of the following relationships is always true?
# Explanation:
## Step1: Analyze parallelogram properties
The sum of the measures of any two consecutive angles in a parallelogram is $180^{\circ}$ because adjacent - angles are supplementary. Diagonals are not always congruent, not all angles are equal (except in rectangles, rhombuses, and squares which are special parallelograms), and opposite angles are equal, not supplementary.
# Answer:
C. The sum of the measures of any two consecutive angles is $180^{\circ}$

### 3. In rectangle $HIJK$, $HI = 4y + 6$ and $JK=5y - 9$. If opposite sides are congruent, what is the value of $y$?
# Explanation:
## Step1: Set up the equation
Since opposite sides of a rectangle are congruent, $HI = JK$. So, $4y + 6=5y - 9$.
## Step2: Solve for $y$
Subtract $4y$ from both sides: $6=y - 9$. Then add 9 to both sides: $y=15$.
# Answer:
A. $15$

### 4. In a parallelogram, the measure of two consecutive angles are $3x + 10^{\circ}$ and $2x+5^{\circ}$. What is the value of $x$?
# Explanation:
## Step1: Use the property of consecutive angles
The sum of two consecutive angles in a parallelogram is $180^{\circ}$. So, $(3x + 10)+(2x + 5)=180$.
## Step2: Simplify the left - hand side
Combine like terms: $5x+15 = 180$.
## Step3: Solve for $x$
Subtract 15 from both sides: $5x=165$. Divide both sides by 5: $x = 33$.
# Answer:
C. $x = 33$

### 5. An interior designer is creating a quadrilateral coffee table with vertices at $A(0,0)$, $B(0,2)$, $C(8, - 2)$, and $D(2,-4)$. Which property can prove that the table is a parallelogram?
# Explanation:
## Step1: Calculate the lengths of the sides
Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Calculate the lengths of $AB$, $BC$, $CD$, and $DA$. If opposite sides are congruent, the quadrilateral is a parallelogram. Diagonals are not congruent, not all angles are right - angles, and opposite sides are not perpendicular.
# Answer:
A. Opposite sides are congruent

### 6. In parallelogram $PQRS$, if diagonal $PR$ is bisected at point $O$ and $PO = 3x+4$ while $OR = 5x - 2$, what is the value of $x$?
# Explanation:
## Step1: Use the property of diagonals in a parallelogram
The diagonals of a parallelogram bisect each other. So, $PO = OR$.
## Step2: Set up the equation
$3x + 4=5x - 2$.
## Step3: Solve for $x$
Subtract $3x$ from both sides: $4 = 2x-2$. Add 2 to both sides: $6 = 2x$. Divide both sides by 2: $x = 3$.
# Answer:
D. $3$

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QUESTION IMAGE

Question

Explanation:

1. In parallelogram \(PQRS\), if angle \(P = 70^{\circ}\), what is the measure of angle \(R\)?

Step1: Recall parallelogram property

Step2: Identify opposite angles

Step1: Analyze parallelogram properties

Step1: Set up the equation

Step2: Solve for \(y\)

Answer:

2. In a parallelogram, which of the following relationships is always true?