Question

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

Answer 1

The answer is 122 or 58

Answer 2

Explanation:

RAGL is a rhombus.

`\therefore RA = AG..</p><p>(sides\: of\: rhombus) \\</p><p> \therefore m\angle ARG = m\angle AGR... (1)`

(Angles opposite to equal sides are equal)

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

Hence, option A is the correct answer.