Question

Find the m∠ARG in rhombus RAGL, given that m∠RAG = 58°.

Answer 1

Step-by-step explanation:

RAGL is a rhombus.

$\therefore RA = AG..(sides\: of\: rhombus) \\ \therefore m\angle ARG = m\angle AGR... (1)$

(Angles opposite to equal sides are equal)

$In\:\triangle RAG, \\m\angle ARG +\bold{ m\angle AGR} + {m\angle RAG} = 180°\\m\angle ARG +\bold {m\angle ARG} + 58° = 180°\\[From\:equation \: (1)]\\2m\angle ARG = 180°-58° \\2m\angle ARG = 122° \\m\angle ARG =\frac{122°}{2} \\\huge \red {\boxed {m\angle ARG = 61°}}$

Hence, option A is the correct answer.

Answer 2

The answer is 122 or 58