CBSE Class 9 Answered
M is a point inside a square ABCD. AMCD is equilateral triangle and MC cuts diagonal DB at E. Then, ZBEC=.....
(1) 75°
(3) 105°
(2) 90°
(4) 60°
Asked by Krishna962511 | 23 Jan, 2023, 10:41: AM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/9cc834fd551d2c45a3eb9aaed8a2122b63ce5e2e7fb0c0.34995762f3.png)
M is a point inside a square ABCD so that ΔMCD is equilateral triangle .
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
In square ABCD, angle between diagonal BD and side DC is 45o .
Hence , we have ,
MDE = 60o -
EDC = 60o - 45o = 15o ............................(2)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
By substituiting
MDE and
EMD in eqn.(1) , we get
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
![begin mathsize 14px style angle end style](https://images.topperlearning.com/topper/tinymce/cache/f1d45fc0daa19a85e39a8446cd27e48f.png)
Answered by Thiyagarajan K | 23 Jan, 2023, 15:55: PM
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