Questions: Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary. x= y=

Transcript text: Find the value of each variable in the parallelogram. Round your answers to the nearest tenth, if necessary. $x=$ $\qquad$ $y=$

Solution

Solution Steps

Step 1: Set up the equation for x

In a parallelogram, consecutive angles are supplementary, meaning they add up to 180°. Therefore, we can set up the following equation: $(x - 5) + (2x + 11) = 180$

Step 2: Solve for x

Combine like terms: $3x + 6 = 180$ Subtract 6 from both sides: $3x = 174$ Divide both sides by 3: $x = 58$

Step 3: Set up the equation for y

In a parallelogram, opposite angles are congruent. Therefore, we can set up the following equation: $2y = 2x + 11$

Step 4: Substitute the value of x and solve for y

Substitute $x = 58$ into the equation: $2y = 2(58) + 11$ $2y = 116 + 11$ $2y = 127$ Divide both sides by 2: $y = \frac{127}{2}$ $y = 63.5$

Final Answer

$x = 58$ $y = 63.5$

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