Question

find the missing angle of the rhombus m angle ADB

Answer 1

$m\angle ADB=41\degree$

Here, we want to calculate the value of m∠ADB

To get this, we use an important property

The property is that the diagonal will bisect the angle

What this mean is that the diagonal splits the angle into the two parts that we can see

Thus, mathematically;

$\begin{gathered} 9x\text{ + 4 = 13x-16} \\ \\ 13x-9x\text{ = 16 + 4} \\ \\ 4x\text{ = 20} \\ \\ x\text{ = }\frac{20}{4} \\ \\ x\text{ = 5} \end{gathered}$

The complete measure of the bisected angle is;

$\begin{gathered} 9x\text{ + 4+13x-16 = 22x-12} \\ \\ \text{Substitute x = 5} \\ \\ we\text{ have;} \\ \\ 22(5)-12\text{ = 110-12 = 98} \end{gathered}$

But this is not we want to calculate

What we want to calculate is the measure of m∠ADB

To get this, we use an important parallelogram property

m∠ADC + 98 = 180

m∠ADC = 180-98

m∠ADC = 82°

An important parallelogarm property as stated above is that the diagonals bisect an angle of the rhombus

So from the diagram;

m∠ADB + m∠CDB = m∠ADC

But from Rhombus angle properties,

m∠ADB = m∠ADC

So we have m∠ADB as 82/2 = 41