Question

In the figure find the value of x, y and z-

Answer 1

Hint: In this problem the properties of triangles will be used. We will try to find the relation between the given angle of ${50^o}$and x, y and z. We will be assuming that the lines m and n and parallel, and the lines p and l are also parallel. Parallel lines are those which do not intersect and remain at an equal distance. The angles of ${50^o}$ and y are corresponding angles of a parallel lines p and l, and y and x form a linear angle. Similarly, the angle of ${50^o}$ and z are corresponding angles of parallel lines m and n. We will use these properties to find out angles.

Complete step-by-step answer:

We have been given the angle of ${50^o}$ which is formed at the intersection of lines l and n. Also, from the figure we can deduce that-
m || n and p || l
Now, we can see that the angles y and ${50^o}$, are corresponding angles between the parallel lines p and l. The corresponding angles are those which lie on corresponding positions between two parallel lines, and are equal to each other. From this property we can write that-
y = ${50^o}$...(1)
Now, both the angles y and x lie on the same line n, which means that the sum of their angles is ${180^o}$. Hence, x and y are linear angles. We can write that-
$x + y = {180^o}$
Using equation (1) we can write that-
$x + {50^o} = {180^o}$$x + {50^o} = {180^o}$
$x = {130^o}$
Now, we can see that angles z is also a corresponding angle with the given angle between the parallel lines m and n, which means that they are also equal. So, we can write that-
z = ${50^o}$

These are the required angles, where x = ${130^o}$, y = ${50^o}$ and z = ${50^o}$.

Note: The definitions of the different types of pairs of angles are often misleading for the students, and they apply the wrong property for the wrong pairs of angles. The first condition for the corresponding angles is that they are always equal between two parallel lines, but students sometimes apply the property as a general case. Students should keep in mind all the necessary conditions for each property.