Question

If two angles of a quadrilateral are 77 degrees and 57 degrees. and out of the remaining two angles. one angle is 10degrees smaller than the other , find these angles.​

Answer 1

Answer:

Let and required one angle of the quadrilateral be X

Then,the other angle be (X-10)

Since,sum of all agles of an quadrilateral is 360°

therefore, 77° + 57° + X + X-10 = 360°

》 134°+ 2X -10 =360°

》 124° + 2X = 360°

》 2X = 360° -124°

》 X = 236°/2

》 X = 118°

Hence, one angle is 118°

and, other angle is 108°.

Step-by-step explanation:

Answer 2

To find : measure of two angles of triangle .

Given : two angles of a quadrilateral are $77$ degrees and $57$ degrees . Out of the remaining two angles. one angle is $10$ degrees smaller than the other  .

Solution :

• As per given condition we know that two angles of a quadrilateral are $77$ degrees and $57$ degrees . Out of the remaining two angles. one angle is $10$ degrees smaller than the other .
• Let , $x$ and $x - 10$ degrees be the remaining two angles .
• We know that sum of measure of fall four angles of quadrilateral is

       $360$°.

• Therefore , we have ,

        $77 + 57 + x + x-10 = 360 \\124 + 2x = 360 \\2x = 360-124 \\2x = 236 \\ x = \frac{236}{2} \\ x= 118$

• Now, missing angles of quadrilateral  are :

       $x =$$118$°

      $x -10 = 118 - 10$ $= 108$°  

Hence , remaining two angles of quadrilateral  are $118$° and $108$° .