Question

what is the value of t?
13t
18t + 18°
t + 46°

Explanation:

Step1: Use 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, \(18t + 18=13t+(t + 46)\)

Step2: Simplify the equation

Expand the right - hand side: \(18t+18=13t+t + 46\)
Combine like terms on the right - hand side: \(18t+18=14t + 46\)

Step3: Solve for \(t\)

Subtract \(14t\) from both sides: \(18t-14t+18=14t-14t + 46\)
\(4t+18=46\)
Subtract \(18\) from both sides: \(4t+18 - 18=46-18\)
\(4t=28\)
Divide both sides by \(4\): \(t=\frac{28}{4}=7\)

Answer:

\(7\)