Question

the diagram shows a convex polygon. what is the value of t? t = \boxed{\space}

Explanation:

Step1: Recall the sum of exterior angles of a convex polygon.

The sum of the exterior angles of any convex polygon is \(360^\circ\). So we can set up the equation: \((4t - 26) + (2t - 34) + (t + 1) + 146 = 360\).

Step2: Simplify the left - hand side of the equation.

First, combine like terms: \(4t-26 + 2t-34+t + 1+146=(4t + 2t+t)+(-26-34 + 1+146)=7t+( - 60 + 147)=7t + 87\).

Step3: Solve for \(t\).

We have the equation \(7t+87 = 360\). Subtract 87 from both sides: \(7t=360 - 87=273\). Then divide both sides by 7: \(t=\frac{273}{7}=39\).

Answer:

\(t = 39\)