Match the given conditions to the number of triangles that can be constructed from them. the measures of two angles are 30 degrees and 60 degrees and the length of the included side is 12 inches

One triangle

Step-by-step explanation:

The angles being fixed at 30° and 60° cause the legs to be fixed.

For the 30° angle, one side is the given side of 12, the other side is at a fixed position.

The same goes for the 60° angle.  

So both missing legs of the triangle are at fixed angles.  The missing angle is 90° (if one is 30° and the other is 60°, then the last angle must add up to 180°, so it is 90°)

Since the last angle is also fixed, it means that there is only one way for the legs to intersect to cause a 90° angle, so there is only one triangle that can be formed

answer: i'm not going to give you the answer, but some hints to work it out.

step-by-step explanation: so, if there is a straight line that means that the line angle is 180°. so we subtract the 2 angle measures provided, (15 and 38) from 180. so the answer is 180 - (38 + 15). (you have to solve the equation)

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: