Question

what is the value of t?

( 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, \(9t + 19=(t + 42)+(t + 33)\)

Step2: Simplify the right - hand side

\((t + 42)+(t + 33)=t + t+42 + 33=2t+75\)
The equation becomes \(9t + 19=2t+75\)

Step3: Solve for \(t\)

Subtract \(2t\) from both sides: \(9t-2t + 19=2t-2t+75\), which gives \(7t+19 = 75\)
Subtract \(19\) from both sides: \(7t+19-19=75 - 19\), so \(7t=56\)
Divide both sides by \(7\): \(t=\frac{56}{7}\)

Answer:

\(8\)