Question

what is the value of $t$?

write your answer as an integer or as a decimal rounded to the nearest tenth.
$t = square^{circ}$

Explanation:

Step1: Apply 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, \(10t - 3=(t + 32)+48\).

Step2: Simplify the right - hand side

Simplify \((t + 32)+48\) to get \(t+80\). The equation becomes \(10t - 3=t + 80\).

Step3: Solve for \(t\)

Subtract \(t\) from both sides: \(10t-t-3=t - t+80\), which simplifies to \(9t-3 = 80\).
Add 3 to both sides: \(9t-3 + 3=80 + 3\), so \(9t=83\).
Divide both sides by 9: \(t=\frac{83}{9}\approx9.2\).

Answer:

\(t = 9.2\)