Question

1. use the information in the figure. if ( mangle f = 116 ), find ( mangle e ). 32 64 116 58

Explanation:

Step1: Use the property of isosceles triangle

Since two sides of \(\triangle DEF\) are equal (marked in the figure), \(\angle D=\angle E\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). So, \(m\angle D + m\angle E+m\angle F=180^{\circ}\). Let \(m\angle E = x\), then \(m\angle D=x\) (because \(\triangle DEF\) is isosceles). Substituting into the angle - sum formula: \(x + x+116^{\circ}=180^{\circ}\), which simplifies to \(2x=180^{\circ}- 116^{\circ}\).

Step3: Solve for \(x\)

\(2x = 64^{\circ}\), so \(x=\frac{64^{\circ}}{2}=32^{\circ}\).

Answer:

32