Two adjacent angle of $| | g m$ are $2 x - 15^{o}$ and $7 x - 75^{o}$ .Find all angles of $| | g m$ ?

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Solution

Adjacent angles of a parallelogram add up to $180^{o}$ , using that:
$2 x - 15^{o} + 7 x - 75^{o} = 180^{o} ⟹ 9 x - 90^{o} = 180^{o}$
$⟹ 9 x = 270^{o} ⟹ x = 30^{o}$
Therefore, the angles are $2 x - 15^{o} = 2 \cdot 30^{o} - 15^{o} = 45^{o}$
Other ange = $180^{o} - 45^{o} = 135^{o}$
As opposite angles of a parallelogram are equal, the other two angles are also $45^{o}$ and $135^{o}$ .

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Column I	Column II
(a) Sum of all the angles of a quadrilateral is	(p) right angles
(b) In a \|\| gm, the angle bisectors of two adjacent angles intersect at	(q) rectangle
(c) Angle bisectors of a \|\| gm form a	(r) 45°
(d) The diagonals of a square are equal and bisect each other at an angle of	(s) 4 right angles

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