Question

what is the value of t? t - 12° t + 20° t - 14°

Explanation:

Step1: Apply triangle - exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the given triangle, if we consider the exterior angle $t + 20^{\circ}$, the two non - adjacent interior angles are $t-12^{\circ}$ and $t - 14^{\circ}$. So, we can write the equation $t + 20=(t - 12)+(t - 14)$.

Step2: Simplify the right - hand side of the equation

$(t - 12)+(t - 14)=t-12+t - 14=2t-26$. So the equation becomes $t + 20=2t-26$.

Step3: Solve for $t$

Subtract $t$ from both sides: $t - t+20=2t - t-26$, which simplifies to $20=t - 26$. Then add 26 to both sides: $20 + 26=t-26 + 26$. So, $t = 46$.

Answer:

$46$