Respuesta :

thaovtp1407

Answer:

m∠J = 67°

m∠T = 67°

m∠G =46°

ST = 5cm

HJ = 3.7cm

Step-by-step explanation:

Given

  • ΔGHJ ≅ ΔSTU
  • GH = 5 cm = GJ
  • m∠GHJ = 67°

=> m∠J = 67°  ( that is the property of isosceles triangle because GH  = GJ

=>  m∠G = 180° - m∠H - m∠J =  180° - 67° - 67° = 46°

  • Because ΔGHJ ≅ ΔSTU

=> GH  = GJ = ST =SU

=> ST = 5 cm

  • Because ΔGHJ ≅ ΔSTU  and GH  = GJ = ST =SU

=> TU = HJ = 3.7 cm

=> m∠T = m∠H = 67°

So:

m∠J = 67°

m∠T = 67°

m∠G =46°

ST = 5cm

HJ = 3.7cm

MrRoyal

Congruent triangles have equal corresponding sides lengths and angle measures.

  • [tex]\mathbf{\angle J = 67^o}[/tex]
  • [tex]\mathbf{\angle T = 67^o}[/tex]
  • [tex]\mathbf{\angle G = 46^o}[/tex]
  • [tex]\mathbf{ST = 5cm}[/tex]
  • [tex]\mathbf{HJ = 3.7cm}[/tex]

Angles H and J are the base angles of ΔGHJ.

So:

[tex]\mathbf{\angle J = 67^o}[/tex]

Angle T in ΔSTU corresponds to angle H.

So:

[tex]\mathbf{\angle T = 67^o}[/tex]

The sum of angles in a triangle is 180 degrees.

So, we have:

[tex]\mathbf{G + H + J = 180^o}[/tex]

Substitute values for H and J

[tex]\mathbf{\angle G + 67 + 67 = 180^o}[/tex]

[tex]\mathbf{\angle G + 134 = 180^o}[/tex]

Subtract 134 from both sides

[tex]\mathbf{\angle G = 46^o}[/tex]

Side length ST corresponds to GH.

So, we have:

[tex]\mathbf{ST = 5cm}[/tex]

Side length HJ corresponds to TU.

So, we have:

[tex]\mathbf{HJ = 3.7cm}[/tex]

Read more about congruent triangles at:

https://brainly.com/question/12413243

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