Question

in a rhombus ABCD, AC=BD.Find the measurement of angle B and angle DCB. ​

Answer 1

Answer:

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Answer 2

∠DCB =  120°

∠B  = 60°

Step-by-step explanation:

Given: ABCD is a rhombus. So AB =  BC  =  CD  = AD. Diagonal AC  =  AD.

Find: Measurement of ∠B and ​∠DCB.

Solution:

In ∆ ABC, AB  =  BC  =  AC.

So ​ΔABC is an equilateral triangle. Hence all internal angles of the equilateral triangle will be 60°.

So, ∠BAC = ∠BCA = ​∠ABC  = 60​°

Similarly, ∆ADC is a equilateral triangle.

So, ∠DAC =  ∠DCA = ​ ​∠ADC  = 60​°

∠DCB = ∠BCA + ∠DCA  = 60​° + 60°

∠DCB =  120°

∠B  = 60°