Answer:
1) x = 21deg, y = 146deg
2) x = 52deg, y = 128deg
3) x = 20deg, y=80deg (assuming we're computing angles of the kite, not of the triangles).
4). a = 116deg, c = 64deg
Explanation:
Problem 1:
The kite is symmetrical, so y = 146deg.
we can compute x as 360deg - 146deg - 146deg - 47deg; because the sum of angles is 360deg in a quadrangle.
360deg - 146deg - 146deg - 47deg = 21deg
Problem 2:
y = 128deg; as it's symmetrical
x = 180deg - y = 52deg
Problem 3:
The smallest triangle has angles y/2, 50deg and 90deg, so
y/2 = 180deg - 90deg - 50deg = 40deg
y = 80deg (this assumes y is the angle of the kite, not half).
Similarily,
x/2 = 180deg - 80deg - 90deg = 10deg
x = 20deg (again, assuming x is the angle of the kite, not half).
Problem 4:
a = 116deg
c = 180deg - 116deg = 64deg (see problem 2).