question_answer

A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus.

A)  \[{{60}^{{}^\circ }},{{120}^{{}^\circ }},{{60}^{{}^\circ }},{{120}^{{}^\circ }}\]    

B)  \[{{45}^{{}^\circ }},{{45}^{{}^\circ }},{{135}^{{}^\circ }},{{135}^{{}^\circ }}\]

C)  \[{{85}^{{}^\circ }},{{95}^{{}^\circ }},{{85}^{{}^\circ }},{{95}^{{}^\circ }}\]                        

D)  \[{{80}^{{}^\circ }},{{100}^{{}^\circ }},{{80}^{{}^\circ }},{{100}^{{}^\circ }}\]

Correct Answer: A

Solution :

(a): From figure, we can see that \[\angle 1=\angle 3={{60}^{{}^\circ }}\] \[\Rightarrow \angle 2=\angle 4={{120}^{{}^\circ }}.\]