m angle A=x+14; m angle D=2x

Answer 1

As others have stated, there is insufficient information to solve this problem, but that shouldn't stop us. Because the two angles given are at points A and D, it is possible that the two angles are part of a four-sided shape. It is unlikely that these angles are adjacent, as they are only named with one letter each. An alternate assumption is that these two angles fall inside of a right triangle.

Assuming that the shape is a quadrilateral, let us also assume what type of quadrilateral it is. With only two angles given, it would be simplest to assume that the shape is some sort of parallelogram. Parallelograms have two pairs of congruent opposite angles, so if we had a shape ABCD, angles A and C would be congruent, and B and D would be congruent. We know that any quadrilateral will have internal angles that sum to 360 degrees. If we sum our angles we get (x+14)+(2x)+(x+14)+(2x)=360, because A and C are congruent and so are B and D. Simplifying this equation we get 6x+28=360. Subtracting 28 from both sides yields 6x=332, which gives us that x = 55.333... degrees.

Alternatively, if we assume that angles A and D are the two other angles of a right triangle, we can use a similar methodology. The interior angles of a triangle sum to 180 degrees. This gives us the equation (x+14)+(2x)+90=180, which simplifies to 3x+104=180. Subtracting 104 from both sides we get 3x=76, resulting in x = 28.666... degrees.

Neither of these assumptions yields integer solutions, so it is likely that this was not the assumption made in the original problem. I hope this response helps you think about possible ways to solve your question.