Question

what is the value of t? diagram of a triangle with two angles labeled ( t - 49^circ ) and a vertical line segment forming an angle ( t ); ( t = square^circ )

Explanation:

Step1: Identify the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, the exterior angle is \(t\) and the two non - adjacent interior angles are both \(t - 49^{\circ}\). So we can write the equation \(t=(t - 49^{\circ})+(t - 49^{\circ})\).

Step2: Simplify the equation

First, expand the right - hand side of the equation: \(t=t - 49^{\circ}+t - 49^{\circ}\). Then, combine like terms: \(t = 2t-98^{\circ}\).

Step3: Solve for \(t\)

Subtract \(t\) from both sides of the equation: \(t - t=2t - t-98^{\circ}\), which gives \(0=t - 98^{\circ}\). Then add \(98^{\circ}\) to both sides: \(t=98^{\circ}\).

Answer:

\(98\)