Question

finding a missing angle
a student drew a triangle with a side length of 14 units and angle measures of 82° and 68°. the triangle is shown here with a missing angle.
∠bac must measure

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle BAC = x\), \(\angle ABC=68^{\circ}\), and \(\angle ACB = 82^{\circ}\).

Step2: Set up the equation

Using the formula \(x+\angle ABC+\angle ACB=180^{\circ}\), substitute the known values: \(x + 68^{\circ}+82^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

First, add \(68^{\circ}\) and \(82^{\circ}\): \(68^{\circ}+82^{\circ}=150^{\circ}\). Then, \(x=180^{\circ}-150^{\circ}\).

Answer:

\(30^{\circ}\)