# a pair of equal angles of rhombus has a measure of 30 degree less than the supplementry angle find the other pair of equal angles of the rhombus

When you know any 1 angle’s measure in a rhombus, you know all 4 angles’ measures. Opposite angles are congruent. And adjacent angles are supplementary - in other words any two adjacent angles sum to 180°. So if we have an angle that measures 60°, the other angles measure 120°, 60°, and 120°.

Now, since the diagonals of a rhombus bisect the pairs of opposite angles, each 120° angle is cut into two 60° angles by the shorter diagonal, forming 2 equilateral triangles within the rhombus, each sharing that shorter diagonal as one of its sides. So the shared side/ diagonal of the rhombus must be the same length as the 4 sides of the rhombus. And since we know the length of the rhombus’s sides is 10 cm, we know that the shorter diagonal is 10 cm as well.

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Done?

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105°
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A pair of equal angle of a rhombus is 30 degree less than the supplementary find the other pair of equal angle of a rhombus? Let say  one Angle of First Pair  = X its given that it another angle is  30 degree less  than the supplementary Supplementary angle = 180 - X but its 30 deg less => 180 -X - 30 = 150 - X => X = 150 - X => 2X = 150° => X = 75° given pair each angle = 75° the other pair of equal angle = 180° - 75° = 105°
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