Question

Q. The angle between the 2 altitudes of a parallelogram through the vertex of an obtuse angle is 50°. Find the angles of a parallelogram.
Class 9th
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Answer 1

Answer:

Suppose PQRS is a parallelogram in which ∠S is obtuse. Through the vertex S altitudes, ST and SU are drawn. Also we have ∠TSU = 60° Now in quadrilateral QTSU, ∠TSU + ∠STQ + ∠TQU + ∠SUQ = 360° (sum of the angles of a quadrilateral) or 60° + 90° + ∠TQU + 90° = 360° ⇒∠TQU = 360° – 240° ⇒∠TQU = 120° ⇒∠PQR = 120° Now ∠PSR = ∠PQR= 120° (opposite angles of a parallelogram) Again ∠QPS + ∠PQR = 180° (adjacent angles of a parallelogram are supplementary) ⇒∠QPS + 120° = 180° ⇒∠QPS = 60° ⇒∠QPS = ∠QRS = 60° (opposite angles of a parallelogram) Hence, angles of the parallelogram are 120°, 60°, 120° and 60 °

hope it helps you

Answer 2

Answer:

consider quadrilateral AMCN

<A+<M+<C+<N=360°

50+90+<C+90=360°

230°+<C=360°

<C=130°

since opposite angles of llgm are equal so <A=<C &<B=<D

<A+<B+<C+<D=360°

2<B+260°=360°

2<B=100°

<B=50°

SO ANGLES OF THE GIVEN llgm will be

<A=130°

<B=50°

<C=130°

<D=50°

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