Question

classify the triangle shown by its angles. justify your reasoning. select choice, the sum of the measures of the three angles of a triangle is select choice. so, (15x + 1) + (6x + 5) + (4x - 1) = select choice. solving for x, x = select choice. substituting select choice into the expressions for each angle, the angle measures are select choice. because the triangle has select choice angle, it is select choice.

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((15x + 1)+(6x + 5)+(4x-1)=180\).
Combine like terms: \((15x+6x + 4x)+(1 + 5-1)=180\), which simplifies to \(25x+5 = 180\).

Step2: Solve for \(x\)

Subtract \(5\) from both sides: \(25x=180 - 5=175\).
Divide both sides by \(25\): \(x=\frac{175}{25}=7\).

Step3: Find the measures of each angle

For the first angle \((15x + 1)\): Substitute \(x = 7\), \(15\times7+1=105 + 1=106^{\circ}\).
For the second angle \((6x + 5)\): Substitute \(x = 7\), \(6\times7+5=42 + 5=47^{\circ}\).
For the third angle \((4x-1)\): Substitute \(x = 7\), \(4\times7-1=28 - 1=27^{\circ}\).

Since one of the angles (\(106^{\circ}\)) is greater than \(90^{\circ}\), the triangle is an obtuse triangle.

Answer:

The triangle is an obtuse triangle.