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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
answered-by-expert Expert Answer
M is a point inside a square ABCD so that ΔMCD is equilateral triangle .
 
begin mathsize 14px style angle end style BEC = begin mathsize 14px style angle end styleMED = 180o - begin mathsize 14px style angle end styleEMD - begin mathsize 14px style angle end styleMDE  .........................(1)
 begin mathsize 14px style angle end styleEMD = 60o
In square ABCD, angle between diagonal BD and side DC is 45o .

Hence , we have , begin mathsize 14px style angle end styleMDE = 60o - begin mathsize 14px style angle end styleEDC = 60o - 45o = 15o ............................(2)
 
By substituiting begin mathsize 14px style angle end styleMDE and begin mathsize 14px style angle end styleEMD in eqn.(1) , we get
begin mathsize 14px style angle end style BEC = 180o - 60o - 15o = 105o  ( Q.E.D )
Answered by Thiyagarajan K | 23 Jan, 2023, 15:55: PM

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