Question

the diagram below shows a triangular parcel of land. the angle measures inside two of the corners of the parcel are labeled. which expression could be used to find x, the measure of the interior angle that represents the third corner of the land? 283° 322° 360 - (283 - 180) + (322 - 180) 180 - (360 - 283) + (360 - 322) 180 - (322 + 283 - 360) 360 - (322 - 283 + 180)

Explanation:

Step1: Recall the property of exterior - interior angles

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. Also, the sum of an interior angle and its corresponding exterior angle is 180 degrees. Let the two given exterior angles be \(283^{\circ}\) and \(322^{\circ}\). The corresponding interior angles are \(180 - 283\) and \(180 - 322\) which is not correct. We know that the sum of the interior angles of a triangle is 180 degrees.
Let the three interior angles of the triangle be \(A\), \(B\), and \(x\). Let the exterior angles corresponding to \(A\) and \(B\) be \(283^{\circ}\) and \(322^{\circ}\). The interior angles corresponding to the given exterior angles are \(360 - 283\) and \(360 - 322\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180 degrees. So \(x=180-[(360 - 283)+(360 - 322)]\).

Answer:

\(180-[(360 - 283)+(360 - 322)]\)