let

a = the first angle of the triangular kite

b = the second angle of the triangular kite

c = the third angle of the triangular kite

a + b + c = 180

the second angle of a triangular kite is four times as large as the first

b = 4a

the third angle is 65 degrees more than the sum of the other two angles

c = 65 + (a + b)

by solving the system of equations

a + b + c = 180

b = 4a

c = 65 + (a + b)

we find

b = 46 degrees

click here to see the step by step solution of the system of equations

the second angle is 46 degrees.