Question

what is m∠1?
diagram: triangle with angle 1, a 36° angle, and an exterior angle of 113°
m∠1 = \boxed{}°
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Explanation:

Step1: Find the adjacent interior angle

The angle of \(113^\circ\) and its adjacent interior angle are supplementary (they form a linear pair), so the adjacent interior angle is \(180^\circ - 113^\circ = 67^\circ\).

Step2: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^\circ\). Let \(m\angle1\) be the measure of angle 1. We know one angle is \(36^\circ\) and the adjacent interior angle we found is \(67^\circ\). So we have the equation \(m\angle1+36^\circ + 67^\circ=180^\circ\).
First, calculate the sum of the known angles: \(36^\circ+67^\circ = 103^\circ\).
Then, solve for \(m\angle1\): \(m\angle1=180^\circ - 103^\circ=77^\circ\).

Answer:

\(77\)