Questions: Inticidgram, DEFG congruent to SPOR. a. Find the value of x. b. Find the value of y.

Inticidgram, DEFG congruent to SPOR. a. Find the value of x. b. Find the value of y.
Transcript text: Inticidgram, DEFG $\cong$ SPOR. a. Find the value of $x$. b. Find the value of $y$.
failed

Solution

failed
failed

Solution Steps

Step 1: Establish Congruent Sides

Given that parallelogram DEFG is congruent to parallelogram PQRS (DEFG $\cong$ PQRS), their corresponding sides and angles are congruent. This means DE $\cong$ SR and GF $\cong$ PS. Also, corresponding angles are congruent, so $\angle G \cong \angle P$, $\angle F \cong \angle S$, $\angle E \cong \angle R$ and $\angle D \cong \angle Q$.

Step 2: Set up an equation to solve for x

Since DE $\cong$ SR, we can set their lengths equal to each other: 8 = 2x - 4

Step 3: Solve for x

Add 4 to both sides of the equation: 12 = 2x Divide both sides by 2: x = 6

Step 4: Set up an equation to solve for y

Since $\angle D \cong \angle Q$, we can set their measures equal to each other: 102 = 6y + x

Step 5: Substitute the value of x and solve for y

Substitute the value of x (6) into the equation from step 4: 102 = 6y + 6 Subtract 6 from both sides: 96 = 6y Divide both sides by 6: y = 16

Final Answer

x = 6, y = 16

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Answer the following for the function f(x)=(x-7)/(x+3). Be sure to show the steps for solving all parts of the problem on your scratchwork in order to receive full credit. Write each answer as an integer or reduced fraction. No decimal numbers, please. 1) Evaluate f(0) 2) Find z so that f(z)=3
failedAnswered
An appliance store decreases the price of a 19-in. television set 28% to a sale price of 459.72. What was the original price? The original price of the television is (Round to the nearest cent.)
failedAnswered
A taste test asks people from Texas and California which pasta they prefer, brand A or brand B. This table shows the results. Brand A Brand B Total ------------------------------------ Texas 80 45 125 California 90 60 150 Total 170 105 275 A person is randomly selected from those tested. What is the probability that the person is from California, given that the person prefers brand A? Round your answer to two decimal places. A. 0.62 B. 0.55 C. 0.53 D. 0.60
failedAnswered
Write the equation of the line through the points (-1,5) and (-1,6).
failedAnswered
(d) lim as x approaches 0 of 3 cos(3x) (e) lim as x approaches 0 of (4x^2) / (x^2 - 3x) (f) lim as t approaches 4 of (t^2 - 16) / (t - 4) (g) lim as t approaches 2 of (5t) / (t - 2) (h) lim as t approaches 4 of 1 / (t(t - 4))