Question

In the adjoining figure find the value of x +y + z + w.

Answer 1

Hint – In order to find the sum of those angles we need to use the property that the sum of angles on a straight line is 180 degrees. Using this will solve our problem and will get the right answer. So using this concept we establish relations between given angles and unknown angles like x,y,z,w. Here we have assumed an interior angle as p.

Complete step-by-step solution -

First we will consider angle x. So from the figure we can say,
80 + x = 180 ………………….(Since sum of angles on a straight line is 180 degrees)
So, x = 100 degrees. …………..(1)
Then we consider angle y. So, y + 130 = 180
y = 50 degrees. …………..(2)
Then we consider z. So, z + 70 = 180
z = 110 degrees. ……………..(3)
To find the angle ‘p’ we will use the concept that the sum of all angles inside a Quadrilateral is 360 degrees.
So we do: 70 + 130 + 80 + p = 360
p = 80 degrees.
Then we can say angle p and w are on the same line so
p + w =180 degrees
So, w = 180 – 80 =100 degrees ……………..(4)

So, from (1), (2), (3) and (4) we can say that
x + y + z + w = 100 + 50 + 110 + 100 = 360 degrees.
Hence the answer to this problem is 360 degrees.

Note – Whenever we face such types of problems we should know that the sum of all angles inside a quadrilateral is 360 degrees and the sum of interior angle and exterior angle with respect to the same line is 180. Using this concept will solve our problem and will get the right answer.