Question

link to desmos graphing calculator
given the isosceles triangle below with sides and angles as marked, determine ( mangle n ).
( mangle n=square^{circ} )

Explanation:

Step1: Find the base angles of the isosceles triangle

In an isosceles triangle, the base angles are equal. Let the base angles be \(x\). Using the angle - sum property of a triangle (\(38^{\circ}+x + x=180^{\circ}\)), we get \(38^{\circ}+2x = 180^{\circ}\). Solving for \(x\):

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Step2: Use the exterior - angle property

The exterior angle \(n\) is equal to the sum of the two non - adjacent interior angles. Here, the non - adjacent interior angle to \(n\) is \(38^{\circ}\) and the other non - adjacent interior angle is equal to the base angle of the isosceles triangle. But we can also use the linear - pair property. Since the base angle of the isosceles triangle is \(71^{\circ}\), and \(n\) and the base angle form a linear pair (\(n + 71^{\circ}=180^{\circ}\)), then \(n=180^{\circ}-71^{\circ}\)

Answer:

\(109\)