Question

what is the value of x?

Explanation:

Step1: Identify the triangle type

The triangle is isosceles (two sides are equal), so the base - angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the measure of \(\angle J=x\) and \(\angle I = x\) (base - angles of isosceles triangle), and \(\angle K = 78^{\circ}\). Then \(x + x+78^{\circ}=180^{\circ}\).

Step3: Solve the equation

Combine like terms: \(2x+78^{\circ}=180^{\circ}\). Subtract \(78^{\circ}\) from both sides: \(2x=180^{\circ}- 78^{\circ}=102^{\circ}\). Divide both sides by 2: \(x=\frac{102^{\circ}}{2}=51^{\circ}\).

Answer:

\(51\)