Question

LOTS OF POINTS, please answer it!

Answer 1

Measure of angle PSQ = 12.5 (degree).

Explanation:

Given:

A quadrilateral PQRS.

Exterior angle at Q = 155 (degree)

To find measure of angle PSQ.

Let the
`m\angle\ PSQ` be
`x`

According to the question.

As
`m\angle \ Q =155`

Adjacent angle to
`Q` is
`= (180-155)=25` [Using linear pair].

Note:Property of a parallelogram:

Diagonally opposite angles of a quadrilateral are equal.

Measure of
`\angle S` is equal to the measure of
`\angle Q`. [They are diagonally opposite].

`m\angle S=m\angle Q=25\deg`

`m\angle S =m\angle PSQ + m\angle QSR`

And
`m\angle PSQ=m\angle QSR` [Diagonal are angle bisector at the vertex]

`m\angle S=m\angle PSQ +m\angle PSQ`

`m\angle S= 2*m\angle PSQ`

`(m\angle S)/(2) =m\angle PSQ`

`(25)/(2) =m\angle PSQ`

`12.5=m\angle PSQ`

So measure of angle PSQ = 12.5 (degrees).