Question

How do I find the answe for this example

Answer 1

in a rhombus, the diagonals bisect each other, namely they cut each other in halves, and also they cut their vertices in half too.

what does that mean? well, it means that the two angles at the vertex F are twins, thus 8x - 49 = 5x - 7.


`\bf 8x-49=5x-7\implies 3x=42\implies x=\cfrac{42}{3}\implies x=14\\\\ -------------------------------\\\\ \measuredangle IFG\implies 5(14)-7\implies 63^o`

now, the diagonals in a rhombus also meet each other at a right angle, therefore, on the triangle FIG, ∡F is 63°, ∡I is 90° and ∡G is 180 - ∡F - ∡I.