The three angles add to 180 degrees. Also , the two base angles of the isoscele triangle are equal, ..
Set those base angles equal, and solve for x.
Put that value of x into the given, and compute the base angles.
The third angle will be the amount to add to the two base angles to get 180 deg
how do I find the vertex angle of an isosceles triangle with base angles of (4x-9) and (3x+2).
45 degrees 45 degrees and 90 degrees
To find the vertex angle of an isosceles triangle with base angles (4x-9) and (3x+2), you can follow these steps:
1. Start by setting the two base angles equal to each other:
(4x-9) = (3x+2). This is because the base angles of an isosceles triangle are equal.
2. Solve the equation for x:
Start by simplifying the equation by combining like terms:
4x - 9 = 3x + 2.
Next, isolate the variable x by moving all terms with x to one side of the equation:
4x - 3x = 2 + 9.
Simplify the equation further:
x = 11.
3. Substitute the value of x back into one of the base angle expressions to find the actual measure of the base angles.
For example, substitute x = 11 into (4x-9):
Base angle = (4 * 11) - 9 = 44 - 9 = 35 degrees.
4. Now, since you know that the base angles are equal and each measures 35 degrees, you can calculate the vertex angle by subtracting the sum of the base angles from 180 degrees:
Vertex angle = 180 - (35 + 35) = 180 - 70 = 110 degrees.
Therefore, the vertex angle of the isosceles triangle is 110 degrees.