Question

1. find the measure of angle e

explain the mistake.
find the correct answer.

Explanation:

Step1: Find the adjacent angle of \(152^{\circ}\)

The adjacent angle of \(152^{\circ}\) is \(180 - 152=28^{\circ}\) (linear - pair angles).

Step2: Use the angle - sum property of a triangle

In \(\triangle DEF\), we know that the sum of interior angles of a triangle is \(180^{\circ}\). Let \(\angle D = 60^{\circ}\), \(\angle E\) be the angle we want to find and \(\angle F = 28^{\circ}\).
By the formula \(\angle D+\angle E+\angle F = 180^{\circ}\), we can rewrite it as \(\angle E=180-(60 + 28)\).

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Step3: Analyze the mistake

The mistake is that \(152-66 = 86\) is incorrect. There is no geometric basis for subtracting \(66\) from \(152\). The correct approach is to first find the angle adjacent to \(152^{\circ}\) (using the linear - pair property) and then use the angle - sum property of a triangle.

Answer:

The measure of \(\angle E\) is \(92^{\circ}\). The mistake was using an incorrect arithmetic operation (\(152-66\)) without a geometric justification. The correct steps involve using linear - pair angles and the angle - sum property of a triangle.