Question

if ABCD is a rhombus find the measure of angleADC given that angle BAC = 55°

Answer 1

Given,
BAC = 55°
TO FIND angle ADC
In rhombus ABCD
AB = AC
Therefore, angle BAC = angle BCA = 55°
In ∆ ABC, we have
BAC + BCA + ABC = 180°
55° + 55° + ABC = 180°
110° + ABC = 180°
ABC = 70°
Now, as we know that opposite angle of a rhombus are equal.
Therefore, ABC = ADC = 70°
Hence, measure of ADC is 70°.