Question

a
x + 23
80°
4x + 17

Explanation:

Step1: Use the 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, \(4x + 17=(x + 23)+80\).

Step2: Simplify the equation

$$
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$$

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(4x - x+17=x - x+103\), which gives \(3x+17 = 103\). Then subtract 17 from both sides: \(3x+17-17=103 - 17\), so \(3x=86\). Divide both sides by 3: \(x=\frac{86}{3}\approx28.67\).

Answer:

\(x=\frac{86}{3}\)