Question

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what is the measure of an exterior angle in a regular triangle?
write your answer as an integer or as a decimal rounded to the nearest tenth.

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Explanation:

Step1: Recall properties of regular triangle

A regular triangle (equilateral triangle) has all interior angles equal. The measure of each interior angle of an equilateral triangle is \(60^\circ\).

Step2: Use linear pair for exterior angle

An exterior angle and its adjacent interior angle form a linear pair, so they are supplementary (sum to \(180^\circ\)). Let the exterior angle be \(x\). Then \(x + 60^\circ= 180^\circ\). Solving for \(x\), we get \(x = 180^\circ - 60^\circ=120^\circ\). Also, for any regular polygon, the measure of each exterior angle can be calculated by \(\frac{360^\circ}{n}\), where \(n\) is the number of sides. For a triangle, \(n = 3\), so \(\frac{360^\circ}{3}=120^\circ\).

Answer:

\(120\)