Question

Find the measure of all the angles of a parallelogram, if one angle is 24° less than twice the smallest angle

Answer 1

Let one angle be x and second angle be y.
Then , the 3rd angle will be equal to 1st angle and the 2nd angle will be equal to the 4th angle because in a ||gm, opposite angles are equal.
=> x + x + y + y = 360°. ( by angle sum property)
= 2x + 2y = 360°
= x + y = 180° .....(1)
Also, x - 2y = -24° ......(2)
(1) - (2)
= 3x = 204
= x = 68°
Put this value in eq (1)
68° + y = 180°
y = 180° - 68°
y = 112°
Therefore the angles are 68°, 112°, 68°, 112°.
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