Question

question 2 of 10
what is the measure of \\( \angle e \\), in degrees?

a. \\( 155^{circ} \\)
b. \\( 125^{circ} \\)
c. \\( 130^{circ} \\)
d. cannot be determined

Explanation:

Step1: Identify the triangle type

Since \( DE = EF = 10 \), \(\triangle DEF\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, \(\angle D=\angle F = 25^{\circ}\).

Step2: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle E=x\). Then, by the angle - sum property of a triangle \(x+\angle D+\angle F = 180^{\circ}\).
Substitute \(\angle D = 25^{\circ}\) and \(\angle F = 25^{\circ}\) into the equation: \(x+25^{\circ}+25^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(x + 50^{\circ}=180^{\circ}\).
Solve for \(x\): \(x=180^{\circ}-50^{\circ}\).

Answer:

\(130^{\circ}\), so the answer is C.