Question

find the value of x in the triangle shown below.
x =
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Explanation:

Step1: Identify the triangle type

The triangle has two sides of length 7, so it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let the two base - angles be \(x\) (the angle we want to find) and the other base - angle. The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the equation

We know that the sum of angles in a triangle is \(x + x+80^{\circ}=180^{\circ}\). Combining like terms, we get \(2x+80^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(80^{\circ}\) from both sides of the equation: \(2x=180^{\circ}-80^{\circ}\). So \(2x = 100^{\circ}\). Then divide both sides by 2: \(x=\frac{100^{\circ}}{2}\).

Answer:

\(50\)