Question

refer to the figure.
if ( mangle fde=(3x - 15)^{circ} ) and ( mangle fdb=(5x + 59)^{circ} ), find the value of ( x ) such that ( angle fde ) and ( angle fdb ) are supplementary.
( x = )

Explanation:

Step1: Use the property of supplementary angles

If two angles are supplementary, their sum is \(180^{\circ}\). So, \(m\angle FDE + m\angle FDB=180^{\circ}\).
Substitute the given expressions: \((3x - 15)+(5x + 59)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+5x-15 + 59=180\), which simplifies to \(8x+44 = 180\).

Step3: Solve for \(x\)

Subtract 44 from both sides: \(8x=180 - 44\), so \(8x=136\).
Divide both sides by 8: \(x=\frac{136}{8}\).

Answer:

\(x = 17\)