The quadrilateral is a rectangle, all of its corner angles are rigth angles.
5)
m∠DAC=2x+4
m∠BAC=3x+1
Both angles are complementary, which means that they add up to 90º
You can symbolize this as:
Replace the expression with the given measures for both angles:
Now you have established a one unknown equation.
Solve for x:
Next is to calculate the measure of m∠BAC, replace the given expression with x=17
m∠BAC=3x+1= 3*17+1=52º
6)
m∠BDC=7x+1
m∠ADB=9x-7
Angle m∠BDC is a corner angle of the rectangle, as mentioned before, all corner angles of a rectangle measure 90º, so there is no need to make any calculations.
Note: the diagonals of the rectangle bisect each corner angle, this means that it cuts the angle in half, so m∠BDC=2*(m∠ADB)