Question

a triangle has interior angles of 44° and 57°. what is the measure of the third interior angle of the triangle?

Explanation:

Step1: Recall triangle angle sum property

The sum of interior angles of a triangle is \(180^\circ\). Let the third angle be \(x\).

Step2: Set up the equation

We know two angles are \(44^\circ\) and \(57^\circ\). So, \(44^\circ + 57^\circ + x = 180^\circ\).

Step3: Calculate the sum of known angles

First, find the sum of \(44^\circ\) and \(57^\circ\): \(44 + 57 = 101\), so the sum of the two known angles is \(101^\circ\).

Step4: Solve for the third angle

Subtract the sum of the known angles from \(180^\circ\): \(x = 180^\circ - 101^\circ = 79^\circ\).

Answer:

The measure of the third interior angle is \(79^\circ\).