Question

geometry: section 7 ▶ unit 3: triangle properties
18: isosceles & equilateral triangles
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question 5 (1 point)
find the value of x.

x =
blank 1:

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the sides opposite equal angles are equal. Here, since the two base angles are \(78^{\circ}\) each, the two sides \(4x + 23\) and \(10x-1\) are equal. So, we set up the equation \(4x + 23=10x - 1\).

Step2: Solve the equation 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:

\(4\)