If mA = x2, mC = 154°, and mD = 15x, what is mA?

Question

triangles in geometry

Answer 1

In the triangle ACD the angles must sum to 180°, so:

x²+154+15x=180,

x²+15x=180-154=26,

x²+15x+225/4=26+225/4, completing the square,

(x+15/2)²=(104+225)/4=329/4,

x+15/2=√329/2,

x=√329/2-15/2=1.5692° approx.

m∠A=x²=2.4623° approx.

(m∠D=15x=23.5377° approx, and 2.4623+154+23.5377=180.)