1) Two adjacent angles of a parallelogram are in the ratio 5 : 4 find all angles of - Maths - Quadrilaterals

Question

1) Two adjacent angles of a parallelogram are in the ratio 5 : 4
find all angles of the parallelogram
2) ABCD is a rhombus and P , Q , R and S are the mid - point of
the sides AB , BC , CD and DA respectively Show that the
quadrilateral PQRS is a rectangle

ramandeep.singh · Accepted Answer

Q1 Two adjacent angles of a parallelogram are in the ratio 5 : 4 Find all angles of the parallelogram SOL:

We know that Sum of angles on the same side of the transversal is 1800 $∴ ∠ A + ∠ D = 180^{0} \Rightarrow 5 x + 4 x = 180^{0} \Rightarrow x = 20^{0}$ $∴ ∠ A = 5 x = 5 (20^{0}) = 100^{0} ∠ D = 4 x = 4 (20^{0}) = 80^{0}$ As opposite angles of a parallelogram are equal, $∴ ∠ C = 5 x = 5 (20^{0}) = 100^{0} ∠ B = 4 x = 4 (20^{0}) = 80^{0}$ Q2 ABCD is a rhombus and P , Q , R and S are the mid - point of the sides AB , BC , CD and DA respectively Show that the quadrilateral PQRS is a rectangle SOL: The solution is provided in the link: https://www meritnation com/ask-answer/question/abcd-is-a-rhombus-and-p-q-r-and-s-are-the-mid-points-of-the/math/476823 Hope you get it

1) Two adjacent angles of a parallelogram are in the ratio 5 : 4 . find all angles of the parallelogram . 2) ABCD is a rhombus and P , Q , R and S are the mid - point of the sides AB , BC , CD and DA respectively . Show that the quadrilateral PQRS is a rectangle

1) Two adjacent angles of a parallelogram are in the ratio 5 : 4 . find all angles of the parallelogram .

2) ABCD is a rhombus and P , Q , R and S are the mid - point of the sides AB , BC , CD and DA respectively . Show that the quadrilateral PQRS is a rectangle