Question

In the adjoining figure P Q R S is a rhombus, SQ and PR are the diagonals of the rhombus intersecting at point O. If angle OPQ=35 then find the value of angke ORS+ angle OQP .​

Answer 1

In a rhombus diagonals are perpendicular to each other.

=> angle POQ = 90 degrees

In a rhombus opposite sides are always parallel

so angle QPO = angle ORS = 35 degrees

In triangle OPQ, all angles add upto 180 degrees

=> angle OPQ + angle OQP + angle QOP = 180 degrees

angle OQP = 180 degrees - angle OPQ - angle OQP

angle OQP = 180 - 90 - 35

angle OQP = 55 degrees

Therefore, angle OQP + angle ORS = 35 degrees + 55 degrees

                                                            = 90 degrees

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