Given that triangle ABC is congruent to triangle DEF. If AC=11 m, ED=6 m, EF=15 m, ∠FDE=85
∘
and ∠ABC=55
∘
, then the perimeter of triangle ABC and ∠EFD are, respectively:
- A35 m,45
∘ - B32 m,40
∘ - C30 m,50
∘ - D32 m,45
∘
Solution & Step-by-step Explanation
Since △ABC≅△DEF, their corresponding sides and angles are equal:
AB=DE=6 m
BC=EF=15 m
AC=DF=11 m
Perimeter of △ABC:
Perimeter=AB+BC+AC=6+15+11=32 m
For the angles:
∠CAB=∠FDE=85
∘
∠ABC=∠DEF=55
∘
In △DEF, the sum of angles is 180
∘
:
∠EFD=180
∘
−(∠FDE+∠DEF)
∠EFD=180
∘
−(85
∘
+55
∘
)=180
∘
−140
∘
=40
∘
Thus, the perimeter is 32 m and ∠EFD=40
∘
.
AB=DE=6 m
BC=EF=15 m
AC=DF=11 m
Perimeter of △ABC:
Perimeter=AB+BC+AC=6+15+11=32 m
For the angles:
∠CAB=∠FDE=85
∘
∠ABC=∠DEF=55
∘
In △DEF, the sum of angles is 180
∘
:
∠EFD=180
∘
−(∠FDE+∠DEF)
∠EFD=180
∘
−(85
∘
+55
∘
)=180
∘
−140
∘
=40
∘
Thus, the perimeter is 32 m and ∠EFD=40
∘
.