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: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle FDE + m\angle FDB=180^{\circ}\).
Substitute the given angle - measures: \((3x - 15)+(5x + 59)=180\).

Step2: Combine like terms

\(3x+5x-15 + 59=180\).
\(8x+44 = 180\).

Step3: Isolate the variable term

Subtract 44 from both sides: \(8x+44-44=180 - 44\).
\(8x=136\).

Step4: Solve for x

Divide both sides by 8: \(x=\frac{136}{8}\).
\(x = 17\).

Answer:

17