Questions: If QRST is a kite, find m ∠ QRS.

Transcript text: If $Q R S T$ is a kite, find $m \angle Q R S$.

Solution

Solution Steps

Step 1: Identify congruent angles

Since QRST is a kite, angles R and T are congruent. This means their measures are equal.

Step 2: Set up an equation

Set the expressions for the angle measures equal to each other: 11x - 6 = 4x + 13

Step 3: Solve for x

7x = 19 x = 19/7

Step 4: Calculate the measure of angle T

Substitute the value of x into the expression for angle T: 4(19/7) + 13 = 76/7 + 91/7 = 167/7 degrees.

Step 5: Calculate the measure of angle R

Since angle R is congruent to angle T, its measure is also 167/7 degrees.

Step 6: Calculate the measure of angle S

The sum of the interior angles of a quadrilateral is 360 degrees. Angles Q and S are congruent in a kite. Let y represent the measure of angles Q and S. 2y + 167/7 + 167/7 = 360 2y = 360 - 334/7 2y = 2520/7 - 334/7 2y = 2186/7 y = 1093/7

Step 7: Calculate the measure of angle QRS

The measure of angle QRS is the sum of angles Q and R. Angle QRS = 79 + 167/7 = 553/7 + 167/7 = 720/7

Final Answer

720/7 degrees

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