Question

3 angles of a quadrilateral are in the ratio 1 2 3. The sum of the least and greatest of these angles =180deg. Find all the angles of the quaditrial.

Answer 1

Step-by-step explanation:

Let 1st angle be 1x°,2nd angle be 2x° and 3rd angle of quadrilateral be 3x°.

ATQ,1x+3x=180

or 4x°=180

or x=180/4=45°

So 1st angle=1x°=1×45°=45°

2nd angle=2x°=2×45°=90°

3rd angle=3x°=3×45°=135°

Now the 4th angle of quadrilateral be y°.

We know that the sum of all interior angles of a quadrilateral=360°.

ATQ,45°+90°+135°+y°=360°

or 270°+y°=360°

or y=360-270=90°

So 4th angle of quadrilateral=90°