Answer:
60
Step-by-step explanation:
1. ∠ADC is right angle, then ![m\angle ADC=90^{\circ}.](https://tex.z-dn.net/?f=m%5Cangle%20ADC%3D90%5E%7B%5Ccirc%7D.)
2. Angles ADB and BDC are complementary, then
![m\angle ADB+m\angle BDC=m\angle ADC=90^{\circ}.](https://tex.z-dn.net/?f=m%5Cangle%20ADB%2Bm%5Cangle%20BDC%3Dm%5Cangle%20ADC%3D90%5E%7B%5Ccirc%7D.)
3. You know that ∠BDC is 32° greater than ∠ ADB. Let
then ![m\angle BDC=x+32^{\circ}.](https://tex.z-dn.net/?f=m%5Cangle%20BDC%3Dx%2B32%5E%7B%5Ccirc%7D.)
Since
you have that
![x+x+32^{\circ}=90^{\circ},\\ \\2x=90^{\circ}-32^{\circ},\\ \\2x=58^{\circ},\\ \\x=29^{\circ}.](https://tex.z-dn.net/?f=x%2Bx%2B32%5E%7B%5Ccirc%7D%3D90%5E%7B%5Ccirc%7D%2C%5C%5C%20%5C%5C2x%3D90%5E%7B%5Ccirc%7D-32%5E%7B%5Ccirc%7D%2C%5C%5C%20%5C%5C2x%3D58%5E%7B%5Ccirc%7D%2C%5C%5C%20%5C%5Cx%3D29%5E%7B%5Ccirc%7D.)
This gives you:
Answer:
Cosine = Adjacent/Hypotenuse
Cosine A = 267/391
Cosine^-1 = 267/391
Angle A = 47 degrees.
Let me know if this helps!
A is the answer i hope this heps