Question

find the measure of \\(\angle x\\).

Explanation:

Identify the vertical angles

Using the Vertical Angles knowledge point

$$ \angle \text{opposite to } 32^\circ = 32^\circ $$

Find the adjacent angle on the straight line

Using the Supplementary Angles knowledge point

$$ \angle c = 180^\circ - 32^\circ - 125^\circ = 23^\circ $$

Calculate the measure of angle x

Using the Supplementary Angles knowledge point

$$ \angle x = 180^\circ - \angle c = 180^\circ - 23^\circ = 157^\circ $$

Answer:

\(157^\circ\)