Question
If ABC and DEF are two triangles such that $\triangle\text{ABC}\cong\triangle\text{FDE}$ and $\text{AB}=5\text{m},\angle\text{B}=40^\circ$ and $\angle\text{A}=80^\circ.$ Then, which of the following is true?
✓
Answer
- $\text{DF}=5\text{cm},\angle\text{E}=60^\circ$
Solution:
In $\triangle\text{ABC},$
$\angle\text{C}=180^\circ-\angle\text{A}+\angle\text{B}=180^\circ-80^\circ-40^\circ=60^\circ$
$\triangle\text{ABC}\cong\triangle\text{FDE}$
$\Rightarrow\text{AB}=\text{FD}=5\text{cm}$
$\Rightarrow\angle\text{B}=\angle\text{D}=40^\circ$
$\Rightarrow\angle\text{A}=\angle\text{F}=80^\circ$
$\Rightarrow\angle\text{C}=\angle\text{E}=60^\circ$
$\Rightarrow\text{DF}=\text{FD}=5\text{cm}$ and $\angle\text{E}=60^\circ$
Hence, correct option is (c).
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If AB is a chord of a circle, P and Q are the two points on the circle different from A and B, then:
The side faces of a prism are:
Two chords AB and CD of a circle intersect each other at a point E outside the circle. If AB = 11cm, BE = 3cm and DE = 3.5cm, then CD = ?
- 10.5cm
- 9.5cm
- 8.5cm
- 7.5cm
Each equal side of an isosceles triangle is 13cm and its base is 24cm Area of the triangle is:
If $a^2 + b^2 + c^2 - ab - bc - ca = 0$, than.
→If AB is a chord of a circle, P and Q are the two points on the circle different from A and B, then:
Which of the following points does not lie in any quadrant?
- (1, 7)
- (2, 10)
- (-1, 1)
- (4, 12)
If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is:
