Question

The sum of the interior angles of each polygon is 360 In the diagram, DEFG=SPQR Find the values of x and y

Answer 1

the value of x=2 and the value of y=10

Answer 2

`\( x \)` is equal to 35 degrees, 

`\[ y = 35^\circ \]`

The image shows two trapezoids, DEFQ and FPQS, with some given angle measures and variables for angles in terms of
`\( y \)`. The sum of the interior angles of any quadrilateral is 360 degrees.

To find the value of
`\( y \)`, follow these steps:

Step 1: For trapezoid DEFQ, we set up the equation based on the sum of its interior angles:

`\[ 103^\circ + 81^\circ + (2y + 10^\circ) + (2y + 26^\circ) = 360^\circ \]`

Step 2: Combine like terms and solve for
`\( y \)`:

`\[ 2y + 2y + 103^\circ + 81^\circ + 10^\circ + 26^\circ = 360^\circ \]`

`\[ 4y + 220^\circ = 360^\circ \]`

`\[ 4y = 140^\circ \]`

`\[ y = 35^\circ \]`

Now let's perform these calculations.

The value of
`\( y \)` is 35 degrees. This is found by setting up an equation based on the sum of the interior angles of trapezoid DEFQ and solving for
`\( y \)`.

to find the value of
`\( x \)`, we need to consider trapezoid FPQS.

Step 1: In trapezoid FPQS, we set up an equation based on the sum of its interior angles:

`\[ (3x + 5^\circ) + (2x + 20^\circ) + 90^\circ + 70^\circ = 360^\circ \]`

Step 2: Combine like terms and solve for
`\( x \)`:

`\[ 3x + 2x + 5^\circ + 20^\circ + 90^\circ + 70^\circ = 360^\circ \]`

`\[ 5x + 185^\circ = 360^\circ \]`

Step 3: Subtract 185 from both sides:

`\[ 5x = 360^\circ - 185^\circ \]`

`\[ 5x = 175^\circ \]`

Step 4: Divide by 5 to isolate
`\( x \)`:

`\[ x = (175^\circ)/(5) \]`

Now, let's calculate the value of
`\( x \)`.

The correct value of
`\( x \)` is:

`\[ x = (175^\circ)/(5) = 35^\circ \]`

So,
`\( x \)` is equal to 35 degrees.