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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  RD Sharma | Understanding Shapes (Polygons) Part 142 mins  Basic Understanding of Polygons44 mins  Quadrilaterals32 mins  NCERT | Surface Area of Solid Shapes39 mins  Quiz | Visualising Solid Shapes36 mins  Genius Quiz | Understanding Quadrilaterals20 mins  Quiz | Polygon & their Properties46 mins  NCERT | Understanding Important Laws49 mins  Champ Quiz | Cell44 mins  Understanding Quadrilateral43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 