Question

using 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. (diagram: points a, b, c, d, e, f with lines, not drawn to scale)

Explanation:

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\). So, \(m\angle FDE + m\angle FDB = 180^\circ\).

Step2: Substitute angle measures

Substitute \(m\angle FDE=(3x - 15)^\circ\) and \(m\angle FDB=(5x + 59)^\circ\) into the equation: \((3x - 15)+(5x + 59)=180\).

Step3: Simplify the left - hand side

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

Step4: Solve for x

Subtract 44 from both sides: \(8x=180 - 44=136\). Then divide both sides by 8: \(x=\frac{136}{8}=17\).

Answer:

\(x = 17\)