Question

Given ST|UV and SU || TV, find the measure of each angle below.

Find the angle of STU
Find the angle of TVW

Answer 1

Answer:
`\angle STU=34^(\circ), \angle TVW=116^(\circ)`

Explanation:

By the alternate interior angles theorem,

`3x+4=2x+14\\\\x+4=14\\\\x=10\\\\\implies \angle STU=3(10)+4=\boxed{34^(\circ)}`

By the alternate interior angles theorem,
`\angle UTV=82^(\circ)`, and we also know that
`\angle TUV=34^(\circ)`.

Thus, by the exterior angle theorem,

`\angle TVW=82+34=\boxed{116^(\circ)}`