Question

Find U of trapezoid TUVS

Answer 1

`m\angle U = 103\degree`

Explanation:

`m\angle T + m\angle S = 180\degree` (interior angles on the same side of transversal)

`m\angle T + 77\degree = 180\degree`

`m\angle T = 180\degree- 77\degree`

`m\angle T = 103\degree`

`m\angle U =m\angle T`

(base angles of an isosceles trapezoid)

`m\angle U = 103\degree`

Answer 2

`m<U = 103`

Explanation:

The given trapezoid is an isosceles trapezoid, meaning that the two legs of the trapezoid (sides that intersect the parallel lines) are congruent. One of the proprieties of an isosceles trapezoid is that the opposite angles are supplementary, meaning that the sum of the opposite angles is 180. One can apply this theorem here by stating the following,

`m<S + m<U = 180`

Substitute,

`77+m<U = 180`

Inverse operations,

`77+m<U = 180`

`-77`

`m<U = 103`