Question

find the value of $x$ in the triangle shown below.

$x=\square^{circ}$

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Explanation:

Step1: Use the property of isosceles triangle

Since two sides of the triangle are equal (both 7), the triangle is isosceles. In an isosceles triangle, the base - angles are equal. Let the two base - angles be \(x\) and the vertex - angle be \(80^{\circ}\).

Step2: Apply the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). So, \(x + x+80^{\circ}=180^{\circ}\).
Simplify the equation: \(2x=180^{\circ}- 80^{\circ}\).
\(2x = 100^{\circ}\).
Divide both sides by 2: \(x=\frac{100^{\circ}}{2}\).

Answer:

\(50\)