Question

independent practice: isosceles & equilateral triangles

1. ( x = ) _ find the value of x.

120°

Explanation:

Step1: Find the interior angle of the first isosceles triangle

The exterior angle of a triangle is \(120^{\circ}\). Using the exterior - interior angle relationship (\(180^{\circ}-\text{exterior angle}=\text{interior angle}\)), the interior angle of the first isosceles triangle is \(180 - 120=60^{\circ}\).

Step2: Use the properties of isosceles and equilateral triangles

Since the first triangle has an interior angle of \(60^{\circ}\) and is isosceles (two equal sides), it is an equilateral triangle (all angles in an equilateral triangle are \(60^{\circ}\)). The two triangles are congruent (by SSS - Side - Side - Side congruence, as the sides are marked equal).

Step3: Find the value of \(x\)

Using the vertical - angle and alternate - interior angle relationships and the fact that the triangles are congruent, we know that \(x = 60^{\circ}\)

Answer:

\(60\)