Question

find the measure of angle 1 and then classify the triangle by its angles. 78° 31° 78 and acute 71 and acute 71 and obtuse 78 and right

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle1=x\). Then \(x + 78^{\circ}+31^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

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Step3: Classify the triangle by its angles

Since \(71^{\circ}<90^{\circ}\), \(78^{\circ}<90^{\circ}\), and \(31^{\circ}<90^{\circ}\), all angles of the triangle are acute.

Answer:

71 and Acute