Question

If M angle ABD equals 7X - 31 n m a angles c d b equals 4x + 5 find M angle ABD

Answer 1

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:

`m\angle DAC+m\angle BAC=90º`

Replace the expression with the given measures for both angles:

`(2x+4)+(3x+1)=90`

Now you have established a one unknown equation.

Solve for x:

`\begin{gathered} 2x+4+3x+1=90 \\ 2x+3x+4+1=90 \\ 5x+5=90 \\ 5x=90-5 \\ 5x=85 \\ (5x)/(5)=(85)/(5) \\ x=17 \end{gathered}`

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)