Question

1. find the missing angle measure.

find the correct answer.

explain the mistake:____

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle A=x\), \(m\angle B = 24^{\circ}\), and \(m\angle C=82^{\circ}\). Then the formula is \(x + 24^{\circ}+82^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

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Step3: Analyze the given wrong formula \(m\angle A=24^{\circ}+82^{\circ}\)

The mistake is that the wrong formula \(m\angle A = 24^{\circ}+82^{\circ}\) violates the triangle angle - sum theorem. In a triangle, the sum of all three angles is \(180^{\circ}\), not that one angle is the sum of the other two.

Answer:

The correct measure of \(\angle A\) is \(74^{\circ}\). The mistake in the given \(m\angle A=24^{\circ}+82^{\circ}\) is that it wrongly assumes one angle of a triangle is the sum of the other two, ignoring the fact that the sum of all three interior angles of a triangle is \(180^{\circ}\).