Question

4x + 23 10x - 1 78° 78°

Explanation:

Step1: Set up the equation

Since the triangle has two equal angles (\(78^{\circ}\)), it is an isosceles triangle. In an isosceles triangle, the sides opposite the equal angles are equal. So, we set \(4x + 23=10x - 1\).

Step2: Solve for \(x\)

Subtract \(4x\) from both sides:
\(4x+23 - 4x=10x - 1-4x\)
\(23 = 6x-1\)
Add \(1\) to both sides:
\(23 + 1=6x-1 + 1\)
\(24 = 6x\)
Divide both sides by \(6\):
\(x=\frac{24}{6}\)

Answer:

\(x = 4\)