Two angles of a quadrilateral are $3x\ -\ 4$ each and two are $3x\ +\ 10$ each. Find all four angles of the quadrilateral.

Given: Two angles of a quadrilateral are $3x\ -\ 4$ each and two are $3x\ +\ 10$ each.

To find: We have to find all four angles of the quadrilateral.

Solution:

$2(3x\ -\ 4)\ +\ 2(3x\ +\ 10)\ =\ 360°$

=> $6x\ -\ 8\ +\ 6x\ +\ 20\ =\ 360°$

=> $12x\ +\ 12\ =\ 360°$

=> $x\ +\ 1\ =\ \frac{360}{12}$

=> $x\ +\ 1\ =\ 30$ 

=> $x\ =\ 30\ -\ 1\ =\ 29°$

Now, 

Two angles = $3x\ -\ 4$

Two angles = $3(29)\ -\ 4$

Two angles = $87\ -\ 4$

Two angles = $83°$

Remaining two angles = $3x\ +\ 10$

Remaining two angles = $3(29)\ +\ 10$

Remaining two angles = $87\ +\ 10$

Remaining two angles = $97°$

So, the four angles of the quadrilateral are 83°, 83°, 97°, and 97°.

Tutorialspoint

e

Updated on: 10-Oct-2022

32 Views

Kickstart Your Career

Get certified by completing the course

Get Started