Answer:
1) angle bisector
2) w = 72°
3) t = 44°
4) t = 51°
5) FG = 16 units
Step-by-step explanation:
1) Given that, ∠VYW ≅ ∠WYV
The line which cuts any angle into equal halves is angular bisector of the angle
⇒ YW is angle bisector
2) In a triangle, sum of two interior angle is equal to exterior angle of other side.
⇒ w-41° + w-31° = w.
⇒ w = 72°
3) Sum of interior angles in a pentagon is 540°
(For a n sided it is (n-2)180° )
⇒ 149° + 139° + t+32° + 3t +t = 540°
⇒ t = 44°
4) sum of all exterior angles taken one at each vertex = 360°
⇒ 2t-50° + 46° + 2t + 34° + 2t-50° + 34° + 40° = 360°
⇒ t = 51°
5) Here, by comparing ΔHGF and ΔHIF
∠GHF = ∠IHF
∠HGF = ∠HIF
and HF is common side for both triangles
⇒ ΔHGF ≡ ΔHIF ; i.e) ΔHGF , ΔHIF are congruent triangles
⇒ FG = FI = 16 units
