Question

15 multiple choice 1 point which statement is true about the triangle shown below. w = 99°, because 42 + 39 = 81 and 180 - 81 = 99 w = 261°, because 42 + 39 = 81 and 18 + 81 = 261 w = 81°, because 180 - (42 + 39) = 99 and 180 - 99 = 81 none of the above clear my selection

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
Let's first find the non - adjacent interior angles. The two non - adjacent interior angles are \(42^{\circ}\) and \(39^{\circ}\).
The sum of these two angles is \(42 + 39=81\).
Let the interior angle adjacent to \(w\) be \(x\). Using the angle - sum property of a triangle (\(x+42 + 39=180\)), we get \(x = 180-(42 + 39)=99\).
Since \(x\) and \(w\) are supplementary (\(x + w=180\)), then \(w=180 - x\). Substituting \(x = 99\), we get \(w = 81\).
Another way: Directly using the exterior - angle property (the exterior angle \(w\) is equal to the sum of the two non - adjacent interior angles. Wait, no! Wait, correction: The formula for the exterior angle \(w\): If we consider the linear - pair and angle - sum of a triangle.
Let's re - explain.
The sum of angles in a triangle is \(180^{\circ}\). Let the third interior angle of the triangle be \(y\). Then \(y=180-(42 + 39)=99^{\circ}\).
Since \(y\) and \(w\) form a linear pair (\(y + w=180^{\circ}\)), then \(w=180 - y\).
Substitute \(y = 99^{\circ}\) into the equation \(w=180 - y\), we have \(w=180-99 = 81^{\circ}\).

Answer:

C. \(w = 81^{\circ}\), because \(180-(42 + 39)=99\) and \(180 - 99=81\)