Question

directions: find the value of x. 8. (10x - 11)° (3x - 2)° (3x + 1)° x = 12 10. (11x - 1)° (20x - 3)° 151° x = 5

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Set up equation for the first triangle

For the first triangle with angles \((10x - 11)^{\circ}\), \((3x - 2)^{\circ}\) and \((3x + 1)^{\circ}\), we have the equation \((10x-11)+(3x - 2)+(3x + 1)=180\).
Combining like - terms: \(10x+3x + 3x-11-2 + 1=180\), which simplifies to \(16x-12 = 180\).
Adding 12 to both sides: \(16x=180 + 12=192\).
Dividing both sides by 16: \(x=\frac{192}{16}=12\).

Step3: Set up equation for the second triangle

For the second triangle, we know that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
The exterior angle is \(151^{\circ}\), and the non - adjacent interior angles are \((11x - 1)^{\circ}\) and \((20x - 3)^{\circ}\).
So, \((11x-1)+(20x - 3)=151\).
Combining like - terms: \(11x+20x-1-3 = 151\), which simplifies to \(31x-4 = 151\).
Adding 4 to both sides: \(31x=151 + 4=155\).
Dividing both sides by 31: \(x=\frac{155}{31}=5\).

Answer:

For the first triangle, \(x = 12\); for the second triangle, \(x = 5\)