Kayla4320
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EASY BRAINLIEST PLEASE HELP!!
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EASY BRAINLIEST PLEASE HELP if you answer correctly ill give you brainliest which will give you 100pts if you put links or dont answer accordingly im reporting class=

Respuesta :

msm555

Answer:

Solution given:

Since it is a isosceles trapezoid so it diagonal will be congruent so

PR=QS

PT+RT=12cm

4.9+RT=12cm

RT=12-4.9

RT=7.1cm

PS=QR

QR=9cm

m<QPR=44° base angle of isosceles triangle

m<PTQ=180°-44-44=92°[interior angle remaining of traingle]

m<STR=m<PTQ

m<STR=92°

semsee45

Answer:

RT = 7.1 cm

QR = 9 cm

∠QPR = 44°

∠STR = 92°

Step-by-step explanation:

Properties of an Isosceles Trapezoid

  • Quadrilateral (2 dimensional, 4-sided shape)
  • One pair of parallel sides (bases)
  • One pair of non-parallel sides of equal length
  • Diagonals are the same length
  • Base angles are congruent
  • Opposite angles are supplementary (sum to 180°)
  • Sum of interior angles is 360°

One pair of non-parallel sides of equal length

Therefore:

  • PS = QR = 9cm

Diagonals are the same length

  • QS = PR = 12 cm
  • QT = PT = 4.9 cm

⇒ RT = PR - PT

⇒ RT = 12 - 4.9

⇒ RT = 7.1 cm

Base angles are congruent

Therefore,  ∠TSR = ∠TRS

Interior angles of a triangle sum to 180°

⇒ ∠TSR + ∠STR + ∠TRS = 180°

⇒ 44° + ∠STR + 44° = 180°

⇒ ∠STR = 92°

Using the Alternate Angles Theorem

⇒ ∠TSR = ∠PQT = 44°

As ∠PQT = ∠QPT and ∠QPT = ∠QPR then

⇒ ∠QPR = 44°