Question

choose...67°, 113°, and 84°.48°, 48°, and 84°.25°, 71°, and 84°.22°, 68°, and 84°.choose...emmanuel ischoose...the question.choose one option from each drop - down menu to answerthe triangle arejose...(x - 23)found by solving the equation,is emmanuel correct?

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 23)+(x - 23)+84=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+x)+(23 - 23)+84 = 180\), which simplifies to \(2x+84 = 180\).

Step3: Solve for \(x\)

Subtract 84 from both sides: \(2x=180 - 84\), so \(2x = 96\). Then divide both sides by 2: \(x=\frac{96}{2}=48\).

Step4: Find the angles

Substitute \(x = 48\) into \(x + 23\) and \(x - 23\).
For \(x + 23\): \(48+23 = 71\).
For \(x - 23\): \(48-23 = 25\).

Answer:

The angles of the triangle are \(25^{\circ},71^{\circ},\) and \(84^{\circ}\).