Question

find the value of x.
$x = 2$
$x = 3$
$x = 33$
$x = 52$
$(45x)^{circ}$
$(25x)^{circ}$
$(57 + x)^{circ}$

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. Here, \(\angle TRQ\) is an exterior angle of \(\triangle TRS\). So, \(45x=25x+(57 + x)\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Divide both sides of the equation \(19x = 57\) by \(19\), \(x=\frac{57}{19}=3\).

Answer:

\(x = 3\)