Question

Given that the quadrilateral ABCD is similar to quadrilateral PQRS find the value of the unknown​

Answer 1

Step-by-step explanation:

similar triangles have same angles but different lengths in a ratio

<A=<P

<A=100

<x=180-<A

<x=80

sides are proportional in similar triangles

AD/CD=PS/RS

14/12=y/9

7/6=y/9

21/2=y

Answer 2

The value of the unknowns is x = 80° and y = 10.5 cm.

Given,

Quadrilateral ABCD is similar to quadrilateral PQRS.

To Find,

The value of the unknowns i.e. x and y.

Solution,

For the value of x,

Since quad. ABCD is similar to quad. PQRS

⇒ ∠A = ∠P

⇒ ∠D = ∠S                                           -------------------------------------------(1)

Since the line PQ is parallel to line RS so, the sum of interior angles must be equal to 180°.

⇒ ∠P + ∠S = 180°

⇒ 100° + ∠S = 180°

⇒ ∠S = 180° - 100°

⇒ ∠S = 80°

From (1) we get,

∠D = 80°

⇒ x = 80°

For the value of y,

Since quad. ABCD is similar to quad. PQRS so, the ratio of the corresponding sides must be equal.

⇒ AD/PS = CD/RS

⇒ 14/y = 12/9

⇒ 14/y = 4/3

⇒ y = 14x3/4

⇒ y = 21/2 = 10.5 cm

Therefore, the value of the unknowns is x = 80° and y = 10.5 cm.

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