edited by
670 views

1 Answer

1 votes
1 votes

Given that, $\text{ABCD}$ is a square and $\text{BCE}$ is an equilateral triangle.

Let the side of a square be $x$ cm.


$\angle \text{BCD} = 90^{\circ}, \angle \text{BCE} = 60^{\circ}$

Then $\angle \text{DCE} = 90^{\circ}+60^{\circ} = 150^{\circ}$

Let $\angle \text{CDE} = \angle \text{DEC} = a^{\circ} \quad (\because \text{Angle opposite to the equal sides are equal})$

$\Rightarrow a + a+150^{\circ} = 180^{\circ}$

$\Rightarrow 2a = 30^{\circ}$

$\Rightarrow \boxed{a = 15^{\circ}}$

$\therefore \angle \text{DEC} = 15^{\circ}$

Correct Answer: $\text{A}$

edited by
Answer:

Related questions

0 votes
0 votes
0 answers
1
go_editor asked Mar 11, 2020
468 views
Direction for questions: Answer the questions based on the following information.In a locality, there are five small cities: $\text{A, B, C, D}$ and $\text{E}$. The dista...
1 votes
1 votes
1 answer
2
go_editor asked Mar 11, 2020
668 views
From a circular sheet of paper with a radius $20\:\text{cm}$, four circles of radius $5\:\text{cm}$ each are cut out. What is the ratio of the uncut to the cut portion?$1...
1 votes
1 votes
1 answer
3
go_editor asked Mar 11, 2020
465 views
The points of intersection of three lines $2\text{X} + 3\text{Y} – 5 = 0, 5\text{X} – 7\text{Y} + 2 = 0$ and $9\text{X} – 5\text{Y} – 4= 0$form a triangleare on l...
1 votes
1 votes
1 answer
4
go_editor asked Mar 11, 2020
510 views
The figure shows a circle of diameter $\text{AB}$ and radius $6.5$ cm. If chord $\text{CA}$ is $5$ cm long, find the area of $\triangle \text{ABC}$ __________
1 votes
1 votes
1 answer
5
go_editor asked Mar 11, 2020
554 views
In $\triangle \text{ABC},\:\angle \text{B}$ is a right angle, $\text{AC} = 6$ cm, and $\text{D}$ is the mid-point of $\text{AC}$. The length of $\text{BD}$ is ___________...