Question : ABCD is a rhombus with $\angle$ABC = 52°. The measure of $\angle$ACD is:
Option 1: 54°
Option 2: 26°
Option 3: 48°
Option 4: 64°
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Correct Answer: 64°
Solution : Since opposite angles of a rhombus are equal So, $\angle$ADC = $\angle$ABC = 52° Also, $\angle$DAC = $\angle$DCA = $x$ (say) [since AD = DC] In $\triangle$ ADC, $\angle$ADC + $\angle$DAC + $\angle$DCA = 180° ⇒ $x+x+52°$ = 180° ⇒ $x$ = 64° ⇒ $\angle$DCA = 64° Hence, the correct answer is 64°.
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