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, (x + 23)+(x - 23). the value of x is choose... the angle measures of the triangle are choose...

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, we can set up the equation \(96=(x + 23)+(x - 23)\).

Step2: Simplify the equation

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

Substitute \(x = 48\) into the angle expressions:

• For \(x + 23\): \(48+23 = 71\)
• For \(x - 23\): \(48-23 = 25\)
• The third angle: \(180-(71 + 25)=180 - 96=84\) (using the fact that the sum of angles in a triangle is \(180^{\circ}\))

Answer:

Emmanuel is incorrect. The value of \(x\) is \(48\). The angle measures of the triangle are \(25^{\circ},71^{\circ},84^{\circ}\)