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°
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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