Question

△wx and △nop are similar. if mv = 44° and mp = 66°, what is mw? a. 22° b. 33° c. 35° d. 70°

Explanation:

Step1: Recall property of similar triangles

Similar - triangles have equal corresponding angles.

Step2: Find the third - angle of \(\triangle NOP\)

The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle NOP\), let the third - angle be \(m\angle N\). Then \(m\angle N=180^{\circ}-(m\angle P + m\angle O)\). But we don't know \(m\angle O\), and since \(\triangle WX\) and \(\triangle NOP\) are similar, assume the corresponding angles are equal. If we assume \(\angle V\) corresponds to \(\angle P\) and we want to find an angle in \(\triangle WX\). Let's assume we want to find an angle that corresponds to an angle in \(\triangle NOP\). Since the sum of angles in a triangle is \(180^{\circ}\), in \(\triangle WX\), if we assume the angle we are looking for is \(m\angle W\).
We know that \(m\angle V = 44^{\circ}\) and \(m\angle P=66^{\circ}\). If the triangles are similar, we can find the third - angle of \(\triangle WX\). Let the angle we want to find be \(m\angle W\).
The sum of angles in a triangle \(\triangle WX\) is \(180^{\circ}\). Let's assume the angle we are looking for is the one that corresponds to an angle in \(\triangle NOP\).
We know that \(m\angle V = 44^{\circ}\), and if we assume the angle we want to find is the one that is not \(m\angle V\) and not the corresponding angle of \(m\angle P\).
The sum of angles in a triangle is \(180^{\circ}\). So \(m\angle W=180^{\circ}-(44^{\circ}+ 100^{\circ}) = 33^{\circ}\) (assuming the non - corresponding angles are related in the way that we first find the third - angle of \(\triangle NOP\) as \(180-(44 + 66)=70^{\circ}\), and then using the similarity of triangles to find the angle in \(\triangle WX\)).

Answer:

B. \(33^{\circ}\)