Question

review & refresh
find the value of x.
1.
2.
3.

Explanation:

1.

Step1: Recognize the triangle type

This is an equilateral triangle (all sides equal, so all angles equal).

Step2: Use angle - sum property

Sum of angles in a triangle is \(180^{\circ}\). Since all angles are equal, \(x = 60\).

2.

Step1: Use angle - sum property

Sum of angles in a triangle is \(180^{\circ}\), and one angle is \(90^{\circ}\). Let the two equal angles be \(x\).

Step2: Set up the equation

\(x + x+90=180\). Simplify: \(2x=180 - 90\), \(2x = 90\), \(x = 45\).

3.

Step1: Use the exterior - angle theorem

The exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles.

Step2: Calculate \(x\)

\(x=65 + 48\), \(x = 113\).

Answer:

1. \(x = 60\)
2. \(x = 45\)
3. \(x = 113\)