Q. 24.1( 174 Votes )

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

(i)

(ii)

(iii) left arrow

(iv) 6

(v) beta

Answer :

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

x = 80°


z = x = 80o (Opposite angles are equal)


y = 100° (Opposite angles are equal)


(ii) x, y and z will be complimentary to 500


Hence, required angle = 180 -50


= 1300


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


z = x = 130o (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)

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