Question

erior angles of a triangle
2
(11x + 4)°
128°
8x°
m∠fae =

m∠acd =

Explanation:

Step1: Find the value of \( x \)

Use the exterior - angle theorem of a triangle. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
We know that \( \angle ACD=(11x + 4)^{\circ}\), \( \angle CAB = 8x^{\circ}\), and \( \angle ABC=180 - 128=52^{\circ}\)
By the exterior - angle theorem \(11x + 4=8x+52\)
Subtract \(8x\) from both sides: \(11x-8x + 4=8x-8x + 52\)
\(3x+4 = 52\)
Subtract \(4\) from both sides: \(3x=52 - 4=48\)
Divide both sides by \(3\): \(x = 16\)

Step2: Calculate \(m\angle FAE\)

Since \(x = 16\), and \(m\angle FAE\) and \(8x^{\circ}\) are supplementary (they form a linear pair).
\(m\angle FAE=180-8x\)
Substitute \(x = 16\) into the formula: \(m\angle FAE=180-8\times16\)
\(m\angle FAE=180 - 128=52^{\circ}\)

Step3: Calculate \(m\angle ACD\)

Substitute \(x = 16\) into \(m\angle ACD=(11x + 4)^{\circ}\)
\(m\angle ACD=11\times16+4\)
\(m\angle ACD=176 + 4=180^{\circ}\)

Answer:

\(m\angle FAE = 52^{\circ}\)
\(m\angle ACD=180^{\circ}\)