1. The measures of the angles of a triangle are in the ratio of 2:3:4. What is the measure of the smallest angle?
2. Each side of a rhombus measures 10 inches. If one diagonal of the rhombus is 12 inches long, what is the length of the other diagonal?
The very, very important fact to know here is that you DO NOT NEED to know the sides of a triangle to know the angles. ALL triangles on a plane (perfectly flat surface) have angles that add up to a total of 180 degrees, always.
Since the angles are in the ratio of 2:3:4, let the angles be 2x, 3x, and 4x
So this gives you the equation 2x + 3x + 4x = 180 degrees.
Solve for x, substitute back to get each angle, and check.
Yes, the diagonals do form a vertical angle but that meand the ANGLES are equal, which does NOT tell you about the length of the sides.
I get the feeling here that you have not had lengths versus angle measure explained to you very clearly. This takes illustrations and you should go to a library or bookstore, find a basic math book or ...
The Smallest Angle in 2:3:4 Triangle and Diagonals of a Rhombus are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.