Question

Question 116

In the given figure, find the measures of \(\angle x\) and \(\angle y\).

Answer 1

Since, \(\angle y\) and \(45^\circ\) form a linear pair
So, \(\angle y + 45^\circ = 180^\circ\) [\(\because\) linear pair has sum of \(180^\circ\)]
\(\Rightarrow \angle y = 180^\circ - 45^\circ\)
\(\angle y = 135^\circ\)
\(\therefore\) The sum of all angles in a triangle is equal to \(180^\circ\) So, \(45^\circ + 60^\circ + \angle x = 180^\circ\)
\(\Rightarrow 105^\circ + \angle x = 180^\circ \\
\Rightarrow \angle x = 180^\circ – 105^\circ = 75^\circ\)