The Value of t from given convex polygon is 41.
Explanation:
Let us consider,
a=61°.
b=2t.
c=3t.
d=42°.
e=52°.
The sum of exterior angles of convex polygon is always 360°.
a+b+c+d+e=360°.
The exterior angles of any convex polygon is same as if any angle drawn inside a circle.
Steps to reform the angles:
Step 1: Draw the ∠a as given in the original diagram.
Step 2: The ∠b is adjacent to ∠a 's end and draw a parallel line of ∠b in the ∠a. The angle measure will also be same.
Step 3: Continue the same for next angles ∠c,∠d and ∠e.
(refer the image dotted lines are the parallel lines.)
⇒ 61°+42°+52°+2t+3t=360°.
155°+5t=360°.
5t=205°.
t=41°.
Also,
∠b=82°.
∠c=123°.
Check,
61°+82°+123°+42°+52°=360°.