Question

a corner of a rectangle is cut, creating a trapezoid. what is the value of x? 105° 115° 125° 135°

Explanation:

Step1: Recall the property of a rectangle's angle

A rectangle has four right angles, each \(90^{\circ}\).

Step2: Use the property of the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \(360^{\circ}\). Let the angles of the trapezoid be \(90^{\circ},90^{\circ},45^{\circ},x^{\circ}\).
So, \(90 + 90+45+x=360\).

Step3: Solve the equation for \(x\)

First, simplify the left - hand side: \(225+x = 360\).
Then, subtract \(225\) from both sides: \(x=360 - 225\).
\(x = 135\).

Answer:

\(135^{\circ}\) (the fourth option)