Question

refer to the figure.

figure with points a, b, c, d, e, f; lines: vertical line b-d-e, line a-d-c, line f-d-c (or f-d-a?); note: not drawn to scale

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: Recall supplementary angles property

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

Step2: Substitute the angle expressions

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

Step3: Combine like terms

Combine \(3x\) and \(5x\), \(-15\) and \(59\): \(8x + 44 = 180\).

Step4: Solve for x

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

Answer:

\(17\)