Question

what is the value of a?
d
64°
f
e
a = \square°

Explanation:

Step1: Identify triangle type

The triangle \( DEF \) has two equal - length sides (marked by the tick marks), so it is an isosceles triangle. In an isosceles triangle, the base angles are equal. So \( \angle E=\angle F = a^{\circ} \).

Step2: Use triangle angle sum

The sum of the interior angles of a triangle is \( 180^{\circ} \). So we have the equation \( \angle D+\angle E+\angle F = 180^{\circ} \). We know that \( \angle D = 64^{\circ} \) and \( \angle E=\angle F=a^{\circ} \). Substituting these values into the equation, we get \( 64 + a + a=180 \).

Step3: Solve for \( a \)

Simplify the left - hand side of the equation: \( 64 + 2a=180 \). Subtract 64 from both sides: \( 2a=180 - 64=116 \). Then divide both sides by 2: \( a=\frac{116}{2}=58 \).

Answer:

\( 58 \)