Question

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Explanation:

1. First, note the property of an isosceles - triangle:

• Since the triangle has two equal - side markings, it is an isosceles triangle. In an isosceles triangle, the base angles are equal. So the third angle is also \(40^{\circ}\).

1. Then, use the angle - sum property of a triangle:

• The sum of the interior angles of a triangle is \(180^{\circ}\). So we can set up the equation \((5x + 10)+40 + 40=180\).
• Combine like terms:
• First, simplify the left - hand side of the equation: \(5x+10 + 80=180\), which becomes \(5x+90 = 180\).
• Next, isolate the variable \(x\):
• Subtract 90 from both sides of the equation: \(5x+90−90 = 180−90\), so \(5x=90\).
• Divide both sides by 5: \(\frac{5x}{5}=\frac{90}{5}\), and we get \(x = 18\).

Step1: Identify the triangle type

Isosceles triangle, base angles equal.

Step2: Apply angle - sum property

\((5x + 10)+40 + 40=180\)

Step3: Combine like terms

\(5x+90 = 180\)

Step4: Isolate the variable

\(5x=90\), \(x = 18\)

Answer:

\(x = 18\)