Question

Construct a quadrilateral PQRS in which PQ= 6.5cm, QR=6cm, CD = 4.8cm, ∠P = ∠R =
1000
and ∠S =750

Answer 1

Answer:

75°

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given: In a quadrilateral PQRS, PQ=6.5 cm, QR=6cm, CD=4.8cm and ∠P=∠R=100° and ∠S=75°

To Find: ∠Q and construct a quadrilateral PQRS

Calculation of the angle Q of the quadrilateral PQRS

• Sum of all the angles in a quadrilateral is 360°
• By this statement we can find out the angle Q

   In a quadrilateral,

    ∠P + ∠Q + ∠R + ∠S = 360°

from the given, we know all the angles except ∠Q.

therefore,

   100° + ∠Q   + 100° + 75° = 360°

 By adding all the angle on LHS we'll get,

   275° + ∠Q = 360°

now taking 275° to RHS

 ∠Q = 360° - 275°

  ∠Q = 85°

So we get ∠Q = 85°

Construction of the Quadrilateral PQRS

STEP 1: Draw the segment PQ of length 5cm

STEP 2: Draw angle PQC measuring 85°

STEP 3: With Q as a center draw an arc of radius 6.5cm such that it cuts the side QC

STEP 4: Draw angle QRF measuring 100°

STEP 5: Draw angle QPG measuring 100°

STEP 6: the point where PG and RF intersect is S

Hence, PQRS is the required quadrilateral.