Answers:
Emanuel is not correct
The value of x can be found by solving the equation 96 = (x+23) + (x-23)
The value of x is x = 48
The angle measures of the triangle are 25°, 71°, 84°
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Explanation
Refer to the remote interior angle theorem
This theorem says that adding two interior angles gets us an exterior angle that isn't adjacent to either interior angle used. In visual terms, it's what the diagram is showing.
That's how we can form the equation 96 = (x+23) + (x-23)
The more general form is A+B = C where A,B are interior angles and C is exterior. Angle C is not adjacent to A nor B.
Here's the scratch work to solving that equation.
96 = (x+23) + (x-23)
96 = 2x
x = 96/2
x = 48
Once we know x, we can determine the interior angles.
- x+23 = 48+23 = 71
- x-23 = 48-23 = 25
Notice that these two angles add to 71+25 = 96.
The third interior angle is calculated like this
180-71-25 = 84
or like this
180-(71+25) = 84
This is because the three inside angles of a triangle must add to 180 degrees.
The three interior angles of the triangle are 25°, 71°, 84°
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Extra info (optional)
- The three angles are all less than 90 degrees, so this triangle is acute.
- The triangle is also scalene because all three angles are different in measure.
