Question

the diagram shows a convex polygon.
what is the value of t?
angles: 2t+41°, t+20°, 8t-17°, 2t+38°, 2t+8°

Explanation:

Step1: Identify the property

For a convex polygon, the sum of exterior angles is \(360^\circ\). So we sum all given exterior angles and set equal to \(360\).
Angles: \(2t + 41\), \(t + 20\), \(8t - 17\), \(2t + 38\), \(2t + 8\) (assuming these are all exterior angles, need to confirm the number of sides, but from the diagram, likely 5 - sided, so 5 exterior angles).
Sum: \((2t + 41)+(t + 20)+(8t - 17)+(2t + 38)+(2t + 8)=360\)

Step2: Combine like terms

Combine \(t\) terms: \(2t + t + 8t + 2t + 2t = 15t\)
Combine constants: \(41 + 20 - 17 + 38 + 8 = 41+20=61; 61 - 17 = 44; 44 + 38 = 82; 82 + 8 = 90\)
Equation: \(15t + 90 = 360\)

Step3: Solve for \(t\)

Subtract 90 from both sides: \(15t = 360 - 90 = 270\)
Divide by 15: \(t=\frac{270}{15}=18\)

Answer:

\(t = 18\)