Question

RSTU is a parallelogram.



What is the measure of ∠UST?

Answer 1

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 2

`m\angle UST= 95\°`

Explanation:

Givens:

• 
  `m\angle RSU = 25\°`

• 
  `m\angle STU = 60\°`

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:

`m\angle RSU = m\angle SUT = 25\°`; because they are alternate interior angles.

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

`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\°`