Question

Find the values of angles \[x\], \[y\] and \[z\] in the figure below.

Answer 1

Hint: When two angles are formed such that they are opposite to each other and intersect at a common point or vertex, then they are called vertically opposite angles and are equal.
The angle formed by a straight line is \[180^\circ\].

Complete step-by-step answer:
Consider the figure below,

Here the angle \[x\] and \[58^\circ\] lies in a straight line, therefore they are supplementary angles and their sum is equal to \[180^\circ\].
So, the value of angle \[x\] is,
\[x = 180^\circ - 58^\circ = 122^\circ\].
Now, from the figure it is clear that the angles \[58^\circ\] and \[y\] are vertically opposite angles, therefore they are equal.
So, the value of angle \[y\] is,
\[y = 58^\circ\]
Also, angles \[y\] and \[z\] lie in a straight line, therefore they are supplementary angles and their sum is equal to \[180^\circ\].
So, the value of angle \[z\] is,
\[z = 180^\circ - 58^\circ = 122^\circ\].
Therefore, the values of the angles \[x\], \[y\] and \[z\] are \[122^\circ\], \[58^\circ\] and \[122^\circ\] respectively.

Note: You can determine values of the angles using the result that the sum of angles in a complete cycle is \[360^\circ\]. And the sum of angles in a straight line is \[180^\circ\].