Question

HELP HELP I DONT UNDERSTAND THIS

Answer 1

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