Question

m∠gfe is a straight angle, m∠gfb = (160x)°, and m∠efb = (19x + 1)°, find each measure
diagram: points g, f, e on a straight line (left to right), with f connected to point b below the line
x= blank box°
m∠gfe = blank box°
m∠gfb = blank box°
m∠efb = blank box°

Explanation:

Step1: Recognize straight angle sum

A straight angle is \(180^\circ\), so \(m\angle GFB + m\angle EFB = 180^\circ\). Substitute the given expressions: \(160x + (19x + 1) = 180\).

Step2: Solve for \(x\)

Combine like terms: \(179x + 1 = 180\). Subtract 1: \(179x = 179\). Divide by 179: \(x = 1\).

Step3: Find \(m\angle GFE\)

A straight angle is \(180^\circ\), so \(m\angle GFE = 180^\circ\).

Step4: Find \(m\angle GFB\)

Substitute \(x = 1\) into \(160x\): \(160(1) = 160^\circ\).

Step5: Find \(m\angle EFB\)

Substitute \(x = 1\) into \(19x + 1\): \(19(1) + 1 = 20^\circ\).

Answer:

\(x = 1\)
\(m\angle GFE = 180^\circ\)
\(m\angle GFB = 160^\circ\)
\(m\angle EFB = 20^\circ\)