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?

Question

asked Feb 23, 2023 156k views

1 Answer

Frin · Answer 1 · 2023-02-28T15:08:42+0000

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:

$140^(\circ).$