In a quadrilateral, three angles are 55°, 65°
and 105°
, Find the fourth angle?
Solution: (Ist Method)
We know that
The sum of the four angles of a quadrilateral is 360°.
The sum of the given three angles = 55 + 65+ 105 = 225
The fourth angle = 360 - 225 = 135°.
Example:
The two angles of a quadrilateral are equal with degree measure 76° and the third angle is given as 120°. Find the fourth angle.
Solution: (IInd method)
The sum of the angles of a quadrilateral = 360°.
Let 'x' be then fourth angle.
Therefore 76 + 76 + 120 + x = 360: (Since two of its angles are of 76°).
That is 272 + x = 360:
Therefore x = 360 - 272 = 88°.
Hence the fourth angle is 88°.
Example:
In a quadrilateral, the third angle is 2 times the fourth and the second angle is 3 times the fourth. The first angle is given as 120°. Find the fourth angle.
Solution:
Let the fourth angle be 'x'.
Here, the third angle = 2 times the fourth angle = 2x.
The second angle = 3 times the fourth angle = 3x.
We know the sum of the angles of a quadrilateral = 360°.
Therefore x + 2x + 3x + 120 = 360.
ie 6x + 120 = 360.
ie 6x = 360 - 120 = 240.
ie x = 240 / 6 = 40.
Hence the fourth angle = 40°.
Directions: Read the above example carefully and answer the following questions:
The sum of the first two angles of a quadrilateral is given by 204°. Also given that the third angle is 3 times the fourth. Find the third and fourth angles.
In a quadrilateral, the third angle is 2 times the fourth and the second angle is 3 times the fourth. The first angle is given as 120°. Find the fourth angle.