Questions: Find the value of x, y, and z in the parallelogram below.

Find the value of x, y, and z in the parallelogram below.
Transcript text: Find the value of $x, y$, and $z$ in the parallelogram below.
failed

Solution

failed
failed

Solution Steps

Step 1: Set up the equations

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (add up to 180°). Therefore, we have the following equations:

  1. 87 = -z - 7
  2. 87 + (-5x - 2) = 180
  3. -5x - 2 = y + 2
Step 2: Solve for z

From equation 1: 87 = -z - 7 Add 7 to both sides: 94 = -z Multiply both sides by -1: z = -94

Step 3: Solve for x

From equation 2: 87 - 5x - 2 = 180 Simplify: 85 - 5x = 180 Subtract 85 from both sides: -5x = 95 Divide both sides by -5: x = -19

Step 4: Solve for y

From equation 3: -5x - 2 = y + 2 Substitute the value of x: -5(-19) - 2 = y + 2 Simplify: 95 - 2 = y + 2 93 = y + 2 Subtract 2 from both sides: y = 91

Final Answer

x = -19, y = 91, z = -94

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
RALC CR Biology B The Cycles of Matter Pre-Test Active 1 2 3 4 5 6 7 8 9 10 time remaining 58:34 Which of the following would be a result of eutrophication of a lake? undergrowth of water plants hypoxia, or low levels of oxygen decreased decomposition inactivity of fertilizers Save and Exit Next Submit Mark this and return
failedAnswered
Use the graph, which shows the number of hours Americans sleep, to determine the truth value of each simple statement. Then determine the truth value of the compound statement. It is false that 9% of Americans get 8 hours or more of sleep each night and 32% get 6 hours of sleep each night. What is the truth value of the simple statement "9% of Americans get 8 hours or more of sleep each night"? False True
failedAnswered
Factor the following polynomial. First use a common factor with a positive coefficient, and then use a common factor with a negative coefficient. 2y^3 + 8y^4 + 6y^3
failedAnswered
Plot all of the points of the translated figure. You may click a plotted point to delete it.
failedAnswered
Identify the syntax of the transform property. transform: effect(params); transform: horizontal vertical; transform: radius; transform: size shape at position; Identify the option that defines how positions are measured on the background in the following background property: background: color url(url) position / size repeat attachment origin clip; size origin clip attachment