In an isosceles triangle, the angle between the altitude drawn to the base of the triangle and one leg of the triangle measures 16 less than one base angles of the triangle. find the measure of the vertex angle of this triangle

Step-by-step explanation:

If the diagram is correct, then the third angle of the smallest triangle is 90 degrees.

So the solution for x  is

x + x - 16 +90= 180   Combine the left.

2x + 74 = 180           Subtract 106 from both sides.

2x = 180 - 74

2x = 106                      Divide by 2

2x/2 = 106/2

x = 53

So to get the answer to your question, the 2 base angles are

53 + 53 + y = 180 where y is the apex (or unequal angle).

106 + y = 180             Subtract 74

y = 180 - 106

y = 74