Question

12 $mangle 13 = 4x + 11 =$ _ $mangle 14 = 3x + 1 =$ _

Explanation:

Step1: Solve for \(x\)

Given \(4x + 11=3x + 1\).
Subtract \(3x\) from both sides: \(4x-3x+11=3x - 3x+1\), which simplifies to \(x+11 = 1\).
Subtract \(11\) from both sides: \(x+11-11=1 - 11\), so \(x=-10\).

Step2: Find \(m\angle13\)

Substitute \(x = - 10\) into \(4x + 11\).
\(4\times(-10)+11=-40 + 11=-29\). But angles can't be negative. There is a mistake in the initial assumption. Actually, \(\angle13\) and \(\angle14\) are supplementary (they form a linear - pair). So \(4x + 11+3x + 1=180\).
Combine like terms: \(7x+12 = 180\).
Subtract \(12\) from both sides: \(7x=180 - 12=168\).
Divide both sides by \(7\): \(x = 24\).

Step3: Calculate \(m\angle13\)

Substitute \(x = 24\) into \(4x + 11\).
\(m\angle13=4\times24+11=96 + 11=107\).

Step4: Calculate \(m\angle14\)

Substitute \(x = 24\) into \(3x + 1\).
\(m\angle14=3\times24+1=72 + 1=73\).

Answer:

\(m\angle13 = 107\), \(m\angle14 = 73\)