Question

△lig≅△zhj. if m∠i = 98° and m∠l = 6°, find m∠j.
answer attempt 1 out of 5
m∠j can be determined. m∠j =
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Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle LIG\), we know \(m\angle I = 98^{\circ}\) and \(m\angle L=6^{\circ}\). Let \(m\angle G=x\). Then \(m\angle I + m\angle L+m\angle G = 180^{\circ}\).

Step2: Calculate \(m\angle G\)

Substitute the known values into the angle - sum formula: \(98^{\circ}+6^{\circ}+x = 180^{\circ}\). Simplify the left - hand side: \(104^{\circ}+x = 180^{\circ}\). Solve for \(x\): \(x=180^{\circ}- 104^{\circ}=76^{\circ}\).

Step3: Use congruent triangles property

Since \(\triangle LIG\cong\triangle ZHJ\), corresponding angles are equal. \(\angle J\) corresponds to \(\angle G\). So \(m\angle J=m\angle G\).

Answer:

76