Question

error analysis describe and correct the error in finding ( mangle 1 ).
( 115^circ + 39^circ + mangle 1 = 360^circ )
( 154^circ + mangle 1 = 360^circ )
( mangle 1 = 206^circ )

Explanation:

Step1: Identify the shape (triangle)

The figure is a triangle, so the sum of interior angles is \(180^\circ\), not \(360^\circ\).

Step2: Set up the correct equation

For a triangle, \(115^\circ + 39^\circ + m\angle1 = 180^\circ\)

Step3: Solve for \(m\angle1\)

First, calculate \(115^\circ + 39^\circ = 154^\circ\). Then, \(m\angle1 = 180^\circ - 154^\circ = 26^\circ\)

Answer:

The error was using the sum of angles in a quadrilateral (\(360^\circ\)) instead of a triangle (\(180^\circ\)). The correct measure of \(\angle1\) is \(26^\circ\).