Is ABCD a square, given in the question?

I assume ABCD is a square.

So AB = BC = CD = AD and the 4 angles are all right angles (90°)

AC is the diagonal of the square, and it divides the square into 2 isosceles right-angled triangles ABC and ADC.

∠CAB = ∠BCA = 45° , they are base angles of the same isosceles triangle since AB = BC

( Or (180° - 90°)/2 = 45°)


∠YAB = ∠CAB - 19°
= 45° - 19°
= 26°

Since AB = AY, triangle ABY is isosceles
∠ABY = ∠AYB (base angles of the same isosceles triangle)

∠ABY = (180° - ∠YAB)/2

= (180° - 26°)/2

= 154° / 2

= 77°

And since AB = AY and AB = AD,

Then AY = AD

So triangle AYD is also isosceles.

∠AYD = ∠ADY (base angles of the same isosceles triangle)

∠DAY = ∠DAC + ∠ CAY
= 45° + 19°
= 64°

∠AYD = (180° - 64°)/2 = 58°

∠CDY = ∠ADC - ∠AYD
= 90° - 58°
= 32°

Edited

The working is correct, but 90-58=32. :)

Already edited 7 mins ago. Your app still showing 22°?

Yes still 22, even after seeing this message.

Maybe your app needs an update or reinstall. It's showing 32 online as well in addition to app