Question

find the value of x.

x = 2
x = 3
x = 33
x = 52

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, \((45x)^{\circ}\) is an exterior angle of \(\triangle TRS\), and the two non - adjacent interior angles are \((25x)^{\circ}\) and \((57 + x)^{\circ}\). So, \(45x=25x+(57 + x)\).

Step2: Simplify the equation

First, expand the right - hand side: \(45x=25x+57 + x\).
Combine like terms on the right - hand side: \(45x=26x + 57\).
Subtract \(26x\) from both sides: \(45x-26x=26x + 57-26x\).
We get \(19x=57\).

Step3: Solve for \(x\)

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

Answer:

\(x = 3\)