Question

11/7 - isosceles and equilateral practice
7 of 20
possible points: 0.8
what is the value of x?
x=

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle \( \triangle DEF\) (\(DE = EF\)), the base - angles are equal (\(\angle D=\angle F=x^{\circ}\)). Also, the sum of interior angles of a triangle is \(180^{\circ}\). So, \(\angle D+\angle F+\angle E = 180^{\circ}\).

Step2: Substitute the known angle value

We know that \(\angle E = 56^{\circ}\), and \(\angle D=\angle F=x^{\circ}\). Then the equation becomes \(x + x+56=180\).
Simplify the left - hand side: \(2x+56 = 180\).
Subtract 56 from both sides: \(2x=180 - 56\).
\(2x=124\).
Divide both sides by 2: \(x=\frac{124}{2}\).

Answer:

\(62\)