Question

a carpenter cuts the corners of a rectangle to make the trapezoid shown.
what is the value of x?
○ 5.375
○ 5.5
○ 11
○ 13

Explanation:

Step1: Identify the relationship

Since the original figure is a rectangle, adjacent angles are supplementary. After cutting, the two angles \( (9x)^\circ \) and \( (7x + 4)^\circ \) should be supplementary (their sum is \( 180^\circ \)) because they are adjacent angles in the trapezoid formed from the rectangle. So we set up the equation:
\( 9x + 7x + 4 = 180 \)

Step2: Combine like terms

Combine the \( x \)-terms:
\( 16x + 4 = 180 \)

Step3: Solve for \( x \)

Subtract 4 from both sides:
\( 16x = 180 - 4 \)
\( 16x = 176 \)

Divide both sides by 16:
\( x = \frac{176}{16} \)
\( x = 11 \)

Answer:

11