Question

question
in \\( \triangle j k l, \overline{k l} \cong \overline{j k} \\) and \\( m \angle k = 91 ^ { \circ } \\). find \\( m \angle j \\).
answer attempt 1 out of 2

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Explanation:

Step1: Identify the triangle type

Since \( \overline{KL}\cong\overline{JK}\), \(\triangle JKL\) is isosceles. In an isosceles triangle, the angles opposite the equal sides are equal. So, \(\angle L=\angle J\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle J = x\) and \(m\angle L=x\) (because \(\angle J\cong\angle L\) as \(\overline{KL}\cong\overline{JK}\)), and \(m\angle K = 91^{\circ}\). Then \(x + x+91^{\circ}=180^{\circ}\).
Combining like terms gives \(2x+91^{\circ}=180^{\circ}\).
Subtract \(91^{\circ}\) from both sides: \(2x=180^{\circ}- 91^{\circ}=89^{\circ}\).
Divide both sides by 2: \(x=\frac{89^{\circ}}{2}=44.5^{\circ}\).

Answer:

\(44.5^{\circ}\)