Question

solve for x. (equation required) 12) r 40° t m 12x + 12 4 + 8x s

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.
In \(\triangle RST\), \(\angle STM\) (exterior angle) \(=\angle R+\angle S\). So, \(12x + 12=40+(4 + 8x)\).

Step2: Simplify the equation

First, simplify the right - hand side of the equation: \(12x+12=40 + 4+8x\).
\(12x+12=44 + 8x\).
Then, subtract \(8x\) from both sides: \(12x-8x+12=44+8x - 8x\).
\(4x+12=44\).
Next, subtract \(12\) from both sides: \(4x+12 - 12=44 - 12\).
\(4x=32\).

Step3: Solve for \(x\)

Divide both sides of the equation \(4x = 32\) by \(4\): \(x=\frac{32}{4}\).

Answer:

\(x = 8\)