Q. 24.1( 174 Votes )

# Consider the following parallelogram. Find the values of the unknowns x, y, z

(i)

(ii)

(iii)

(iv)

(v)

Answer :

(i) x + 100° = 180° (Adjacent angles are supplementary)

x = 80°

z = x = 80^{o} (Opposite angles are equal)

y = 100° (Opposite angles are equal)

(ii) x, y and z will be complimentary to 50^{0}

Hence, required angle = 180 -50

= 130^{0}

x = y = 130° (Opposite angles are equal)

z = x = 130^{o} (Corresponding angles)

(iii) x = 90° (Vertically opposite angles)

x + y + 30° = 180° (Angle sum property of triangles)

90° + y + 30° = 180°120° + y = 180°

y = 60°

z = y = 60° (Alternate interior angles)

(iv) z = 80° (Corresponding angles)

y = 80° (Opposite angles are equal)

x+ y = 180° (Adjacent angles are supplementary)

x = 180° − 80°

= 100°

(v) y = 112° (Opposite angles are equal in a parallelogram)

x+ y + 40° = 180° (Angle sum property of triangles)

x + 112° + 40° = 180°

x + 152° = 180°

x = 28°

z = x = 28° (Alternate interior angles)

Rate this question :

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