Question

11/7 - isosceles and equilateral practice
possible points: 0.8
find the value of x.
x =

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. In an isosceles triangle (assuming the two marked angles are equal), if the two non - adjacent interior angles are equal, and the exterior angle is \(x\).
Let the two equal non - adjacent interior angles be \(a\). Then \(x=a + a\). Since the side length is given as 15 (assuming the triangle is isosceles with two equal sides and the two non - adjacent interior angles to the exterior angle \(x\) are equal).
If we assume the two non - adjacent interior angles are equal, and by the exterior angle theorem \(x = 2a\). In an isosceles triangle, if we consider the property of angles, and since the two non - adjacent interior angles to \(x\) are equal.
We know that \(x=15 + 15\) (because of the exterior angle theorem for an isosceles triangle where the two non - adjacent interior angles are equal).

Answer:

\(x = 30\)