Question

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find the measure of ∠fgh.

m∠fgh = ______°

Explanation:

Step1: Use exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(3x=(x + 1)+93\)

Step2: Solve for x

Simplify the equation: \(3x=x + 94\)
Subtract \(x\) from both sides: \(3x-x=x + 94-x\), which gives \(2x = 94\)
Divide both sides by 2: \(x=\frac{94}{2}=47\)

Step3: Find \(m\angle FGH\)

Since \(m\angle FGH = 3x\) and \(x = 47\), then \(m\angle FGH=3\times47 = 141\)

Answer:

\(141\)