Question

A building floor plan is shaped like a trapezoid, with two right angle corners. If the third corner is a 40° angle, what is the measure of the fourth angle?

Answer 1

Recall that the interior angles of a regular quadrilateral add up to 360 degrees, and a right angle has a measure of 90 degrees.

Let x° be the measure of the fourth angle, then we can set the following equation:

`40^(\circ)+90^(\circ)+90^(\circ)+x^(\circ)=360^(\circ).`

Adding like terms we get:

`220^(\circ)+x^(\circ)=360^(\circ).`

Subtracting 220 degrees from the above result we get:

`\begin{gathered} 220^(\circ)+x^(\circ)-220^(\circ)=360^(\circ)-220^(\circ), \\ x^\circ=140^\circ. \end{gathered}`

Answer:

`140^(\circ).`