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.... the value of x is choose.... the angle measures of the triangle are choose....

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(96=(x + 23)+(x - 23)\).

Step2: Simplify the right - hand side of the equation

\((x + 23)+(x - 23)=x+23+x - 23=2x\). So the equation becomes \(96 = 2x\).

Step3: Solve for \(x\)

Divide both sides of the equation \(96 = 2x\) by 2. We get \(x=\frac{96}{2}=48\).

Step4: Find the angle measures

The first angle is \(x + 23=48+23 = 71^{\circ}\), the second angle is \(x - 23=48 - 23 = 25^{\circ}\), and the third angle can be found using the fact that the sum of the interior angles of a triangle is \(180^{\circ}\). Let the third angle be \(y\), then \(y=180-(71 + 25)=84^{\circ}\). So Emmanuel is incorrect.

Answer:

Emmanuel is incorrect.
The value of \(x\) can be found by solving the equation \(96=(x + 23)+(x - 23)\).
The value of \(x\) is \(48\).
The angle measures of the triangle are \(25^{\circ},71^{\circ},84^{\circ}\).