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Question

In the given figure : ABCD is a rhombus with angle A=67.
If DEC is an equilateral triangle, calculate CBE
194813_914859a26e2b453593a0b23dfe01636f.png

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Solution

GivenisarhombusABCDwithA=67o&DECisanequilateraltriangle.SoDE=EC=CD&DEC=ECD=CDE=60oAlsoEC=CD=CB[Sinceallsidesoftherhombusareequal]NowA=BCD[Oppositeanglesareequalinarhombus]SoECB=ECD+BCDECB=67o+60oECB=127oSinceEC=CBsoECBisisoscelestriangle.InECB,ECB+BEC+CBE=180o2CBE+1270=1800[BaseanglesinisoscelesareequalCEB=CBE]2CBE=180012702CBE=530CBE=5302
CBE=26.5o

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