Question

given the figure, what is the value of x?
(7x - 16)°
(x + 8)° 48°
a 2 b 12
c 4 d 17.5

Explanation:

Step1: Apply 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, \(7x - 16=(x + 8)+48\).

Step2: Simplify the equation

$$
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$$

Step3: Isolate the variable \(x\)

Subtract \(x\) from both sides: \(7x-x-16=x - x+56\), which gives \(6x-16 = 56\). Then add \(16\) to both sides: \(6x-16 + 16=56+16\), so \(6x=72\). Divide both sides by \(6\): \(x=\frac{72}{6}\).

Answer:

\(x = 12\), so the answer is B.