Question

In the diagram, PQ and ST are parallel lines. Find the value of x.

please help!!​

Answer 1

x = 95°

Explanation:

`m\angle Q = 360\degree - 235\degree = 125\degree \\`

Produce QR In such a way that it intersects ray ST at any point say M.

PQ || ST... (given) and Seg QM is transversal.

`\therefore m\angle PQM + m\angle SMQ = 180\degree \\(interior \: \angle \:Postulate) \\</p><p>\therefore 125\degree + m\angle SMQ = 180\degree \\</p><p>\therefore m\angle SMQ = 180\degree -125\degree \\</p><p>\therefore m\angle SMQ = 55\degree \\</p><p>In\: \triangle SMR, \: x \: is \:exterior \: \angle \\</p><p>\therefore x = 40\degree + 55\degree \\</p><p>\huge \purple {\boxed {\therefore x = 95\degree}}`