Question

1. find ( mangle tef ).

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(25x - 5=18x + 30\).

Step2: Solve the equation for \(x\)

Subtract \(18x\) from both sides: \(25x-18x - 5=18x-18x + 30\), which simplifies to \(7x-5 = 30\).
Add \(5\) to both sides: \(7x-5 + 5=30 + 5\), so \(7x=35\).
Divide both sides by \(7\): \(x=\frac{35}{7}=5\).

Step3: Find \(m\angle TEF\)

Substitute \(x = 5\) into the expression for \(\angle TEF\) (\(25x-5\)).
\(25x-5=25\times5 - 5\).
First, calculate \(25\times5=125\). Then \(125-5 = 120\).

Answer:

\(120^{\circ}\)