Given: triangle NOP is similar to triangle WXY
We know that NOP has a base length of 4 while triangle WXY has a base length of 10
10 / 4 = 2.5
The scale factor = 2.5
We also know that all similar triangles have congruent angles
The measure of angle X on triangle WXY = 58 degrees because its corresponding angle on triangle NOP = 58 degrees.
We know that all the angles of a triangle add up to 180.
The measure of angle P for triangle NOP is:
180 - (49 + 58) = 73 degrees. This means that the measure of angle Y for triangle WXY is also 73 degrees.
We know that the scale factor = 2.5 so 12 / 2.5 = 4.8
NP / WY = 12 / 4.8 = 2.5
The length of WX = 6 * 2.5 = 15
The length of NP = WY / 2.5 = 12 / 2.5 = 4.8
