Question

what is the value of x?
3t
4t
x
5t + 42°
x = □°

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, \(3t + 4t=5t + 42^{\circ}\).

Step2: Solve for \(t\)

Simplify the left - hand side of the equation: \(7t=5t + 42^{\circ}\).
Subtract \(5t\) from both sides: \(7t-5t=5t + 42^{\circ}-5t\), which gives \(2t = 42^{\circ}\).
Divide both sides by 2: \(t=\frac{42^{\circ}}{2}=21^{\circ}\).

Step3: Find \(x\)

Since \(x + 5t+42^{\circ}=180^{\circ}\) (linear pair of angles), substitute \(t = 21^{\circ}\) into the equation.
First, find \(5t+42^{\circ}\): \(5\times21^{\circ}+42^{\circ}=105^{\circ}+42^{\circ}=147^{\circ}\).
Then, \(x=180^{\circ}-(5t + 42^{\circ})\).
So, \(x=180^{\circ}-147^{\circ}=33^{\circ}\).

Answer:

\(33\)