Question

1. solve for x. 5x - 21 3x + 11 9x - 18

Explanation:

Step1: Apply 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, \(9x - 18=(5x - 21)+(3x + 11)\)

Step2: Simplify the right - hand side

Simplify \((5x - 21)+(3x + 11)\):

$$
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$$

The equation becomes \(9x - 18=8x - 10\)

Step3: Solve for \(x\)

Subtract \(8x\) from both sides: \(9x-8x-18=8x - 8x-10\), which gives \(x-18=-10\)
Add \(18\) to both sides: \(x-18 + 18=-10+18\)

Answer:

\(x = 8\)