Q. 45.0( 3 Votes )

# In the adjacent figure *HOPE* is a parallelogram. Find the angle measures *x, y* and *z*. State the geometrical truths you use to find them.

Answer :

∠*HOP +* 70° *=* 180° [Linear pair]

∠*HOP =* 180°-70°

∠*HOP =* 110°

∠*HOP =* ∠*x =* 110° [In a parallelogram opposite angles are equal]

∠*x +* ∠*z + 40° =* 180° [In a parallelogram sum of the adjacent angles is equal to 180°]

110° *+* ∠*z + 40° =* 180°

∠*z =* 180° - 150°

∠*z =* 30°

∠*z +*∠*y = 70°*

∠*y + 30° = 70°*

∠*y = 70°- 30°*

∠*y = 40°*

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

Various types of Force43 mins

Champ Quiz | Cell44 mins

Understanding Quadrilateral43 mins

NCERT | Understanding Important Laws49 mins

Genius Quiz | Understanding Quadrilaterals20 mins

Quiz | Polygon & their Properties46 mins

Types of Friction39 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.

RD Sharma - MathematicsThe angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is

NCERT - Mathematics Exemplar