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Isosceles \& Equilateral
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\( \triangle K L \) is an isosceles triangle with vertex angle \( K \). Find the values of \( x \) and \( y \) if \( J K=8 x, K L=13 x-15, m \angle K J= \) \( (5 y-3)^{\circ} \), and \( m \angle J K L=76^{\circ} \).
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Answer

\( m \angle K = 180^{\circ} - 2(5y - 3)^{\circ} = 76^{\circ} \)

Steps

Step 1 ：\( J K = K L \implies 8x = 13x - 15 \)

Step 2 ：\( m \angle L = m \angle J = m \angle K J = (5y - 3)^{\circ} \)

Step 3 ：\( m \angle K = 180^{\circ} - 2(5y - 3)^{\circ} = 76^{\circ} \)