Question

directions: find the value of x. 8. (10x - 11)° (3x - 2)° (3x + 1)°

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \((10x - 11)^{\circ}=(3x + 1)^{\circ}+(3x - 2)^{\circ}\)

Step2: Simplify the right - hand side

Simplify \((3x + 1)+(3x - 2)\):

$$
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The equation becomes \(10x-11 = 6x-1\)

Step3: Solve for \(x\)

Subtract \(6x\) from both sides: \(10x-6x-11=6x - 6x-1\), which gives \(4x-11=-1\)
Add \(11\) to both sides: \(4x-11 + 11=-1+11\), so \(4x = 10\)
Divide both sides by \(4\): \(x=\frac{10}{4}=\frac{5}{2}=2.5\)

Answer:

\(x = 2.5\)