Question

find the measure of the angle indicated. 11) find ( m angle e ).

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.
In \(\triangle DEF\), \(\angle EDR\) (exterior angle) \(=\angle E+\angle F\). So, \(25x=(11x - 1)+85\).

Step2: Solve the equation for \(x\)

Simplify the right - hand side of the equation: \(25x=11x - 1 + 85\), which becomes \(25x=11x+84\).
Subtract \(11x\) from both sides: \(25x-11x=11x + 84-11x\), so \(14x=84\).
Divide both sides by \(14\): \(x=\frac{84}{14}=6\).

Step3: Find the measure of \(\angle E\)

Substitute \(x = 6\) into the expression for \(\angle E\). The measure of \(\angle E=11x-1\).
\(\angle E=11\times6 - 1=66 - 1=65^{\circ}\).

Answer:

\(65^{\circ}\)