Q. 24.3( 12 Votes )

The following figures are parallelograms. Find the degree values of the unknowns x, y, z.


Answer :

(i) ABC = Y = 100° [In a parallelogram opposite angles are equal]

x + Y = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]


x + 100° = 180°


x = 180°-100°


x = 80°


x = z = 80° [In a parallelogram opposite angles are equal]


(ii) PSR + Y = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]


Y + 50° = 180°


Y = 180°-50°


Y = 130°


x = Y = 130° [In a parallelogram opposite angles are equal]


PSR = PQR = 50° [In a parallelogram opposite angles are equal]


PQR + Z = 180° [Linear pair]


50° + Z = 180°


Z = 180°-50°


Z = 130°


(iii) In ΔPMN


MPN + PMN + PNM = 180° [Sum of all the angles of a triangle is 180°]


30° + 90° + z = 180°


z = 180°-120°


z = 60°


y = z = 60° [In a parallelogram opposite angles are equal]


z = 180°-120° [In a parallelogram sum of the adjacent angles is equal to 180°]


z = 60°


z + NML = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]


60° + 90°+ x = 180°


x = 180°-150°


x = 30°


(iv) x = 90° [vertically opposite angles are equal]


In ΔDOC


x + y + 30° = 180° [Sum of all the angles of a triangle is 180°]


90° + 30° + y = 180°


y = 180°-120°


y = 60°


y = z = 60° [alternate interior angles are equal]


(v) x + POR = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]


x + 80° = 180°


x = 180°-80°


x = 100°


y = 80° [In a parallelogram opposite angles are equal]


QRS =x = 100°


QRS + Z = 180° [Linear pair]


100° + Z = 180°


Z = 180°-100°


Z = 80°


(vi) y = 112° [In a parallelogram opposite angles are equal]


y + TUV = 180° [In a parallelogram sum of the adjacent angles is equal to 180°]


z + 40° + 112° = 180°


z = 180°-152°


z = 28°


z =x = 28° [alternate interior angles are equal]


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