Question

emmanuel is finding the angles of the triangle in the diagram below. he says that the angles are 48°, 48°, 84°. is emmanuel correct? choose one option from each drop - down menu to answer the question. emmanuel is choose... the value of x can be found by solving the equation, choose... =(x + 23)+(x - 23). the value of x is choose... the angle measures of the triangle are choose...

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we set up the equation \(96+(x + 23)+(x - 23)=180\).

Step2: Simplify the left - hand side of the equation

\[

$$\begin{align*} 96+(x + 23)+(x - 23)&=96+x+23+x - 23\\ &=96 + 2x \end{align*}$$

\]
So the equation becomes \(96+2x = 180\).

Step3: Solve for \(x\)

Subtract 96 from both sides: \(2x=180 - 96\), so \(2x = 84\). Then divide both sides by 2: \(x = 42\).

Step4: Find the angle measures

The angles are \(96^{\circ}\), \((x + 23)^{\circ}=(42+23)^{\circ}=65^{\circ}\), and \((x - 23)^{\circ}=(42 - 23)^{\circ}=19^{\circ}\).

Answer:

Emmanuel is incorrect. The value of \(x\) can be found by solving the equation \(180=(x + 23)+(x - 23)+96\). The value of \(x\) is 42. The angle measures of the triangle are \(96^{\circ},65^{\circ},19^{\circ}\).