Question

a side of the triangle below has been extended to form an exterior angle of 142°, find the value of x.

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). Let the interior angle adjacent to \(142^\circ\) be \(y\). So, \(y + 142^\circ= 180^\circ\). Solving for \(y\), we get \(y = 180^\circ - 142^\circ = 38^\circ\).

Step2: Use triangle angle sum property

The triangle is right - angled, so one angle is \(90^\circ\). Let the angles of the triangle be \(x\), \(y = 38^\circ\) and \(90^\circ\). By the angle - sum property of a triangle (\(x + y+90^\circ = 180^\circ\)), substitute \(y = 38^\circ\) into the equation: \(x+38^\circ + 90^\circ=180^\circ\). Then \(x=180^\circ-(38^\circ + 90^\circ)=180^\circ - 128^\circ = 52^\circ\).

Answer:

\(x = 52^\circ\)