Question

1. 30) find $m\angle c$.

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
For triangle \(ABC\) with exterior angle \(\angle CAE = 122^{\circ}\), we have \(\angle CAE=\angle C+\angle B\).
So, \(122 = 13x+(16x + 6)\).

Step2: Simplify the equation

Combine like terms: \(122=13x + 16x+6\).
\(122=29x + 6\).
Subtract 6 from both sides: \(122−6=29x\).
\(116 = 29x\).

Step3: Solve for \(x\)

Divide both sides by 29: \(x=\frac{116}{29}\).
\(x = 4\).

Step4: Find the measure of \(\angle C\)

Since \(\angle C=13x\), substitute \(x = 4\) into the expression.
\(\angle C=13\times4\).

Answer:

\(52^{\circ}\)