Question

what is the value of t? t =

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $t + 46^{\circ}=(t - 28^{\circ})+(t + 10^{\circ})$.

Step2: Simplify the right - hand side

$(t - 28^{\circ})+(t + 10^{\circ})=t-28^{\circ}+t + 10^{\circ}=2t-18^{\circ}$. So the equation becomes $t + 46^{\circ}=2t-18^{\circ}$.

Step3: Solve for t

Subtract t from both sides: $46^{\circ}=2t - t-18^{\circ}$. Then add $18^{\circ}$ to both sides: $t=46^{\circ}+18^{\circ}$.

Answer:

$t = 64^{\circ}$