Respuesta :

Since it has been split up into triangles we know that 60 and 25 are two angles of each triangle.
add
180 - 85 = 95 degrees ust

Answer:

[tex]m\angle UST= 95\°[/tex]

Step-by-step explanation:

Givens:

  • [tex]m\angle RSU = 25\°[/tex]
  • [tex]m\angle STU = 60\°[/tex]

We know that by definition that parallelogram's angles all sum 360°. If we have a diagonal inside, then, we have two triangles, where their angles sum 180°. Also, in this scenario, we have two parallels being crossed by a transversal, which can allow us to deduct several congruences.

So, from the transversal and parallels, we have:

[tex]m\angle RSU = m\angle SUT = 25\°[/tex]; because they are alternate interior angles.

Now, we consider [tex]\triangle SUT[/tex], where we already know two angles [tex]m\angle SUT = 25\°[/tex] and [tex]m\angle STU = 60\°[/tex]. So, internal angles of a triangle sum 180°, using that we calculate the missing angle ∠UST:

[tex]m\angle UST + m\angle SUT + m\angle UTS = 180\°\\m\angle UST=180\° - m\angle SUT - m\angle UTS\\m\angle UST=180\° - 25\° - 60\°\\\therefore m\angle UST= 95\°[/tex]

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