LOTS OF POINTS, please answer it!

Question

asked May 27, 2021 42.6k views

1 Answer

Stryner · Answer 1 · 2021-05-31T22:11:36+0000

Answer:

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

According to the question.

As
$m\angle \ Q =155$

Adjacent angle to
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).