Question

question
a side of the triangle below has been extended to form an exterior angle of 150°. find the value
of x.
(the image shows a right triangle with one side extended to form a 150° exterior angle, and we need to find the angle x at the other non - right vertex.)

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). The exterior angle (\(150^\circ\)) and the adjacent interior angle of the triangle form a linear pair. Let the adjacent interior angle be \(y\). Then \(y + 150^\circ= 180^\circ\), so \(y = 180^\circ - 150^\circ = 30^\circ\).

Step2: Use triangle angle sum property

A right - angled triangle has one angle of \(90^\circ\). Let the angles of the triangle be \(x\), \(y = 30^\circ\) and \(90^\circ\). The sum of angles in a triangle is \(180^\circ\). So \(x+30^\circ + 90^\circ=180^\circ\).

Step3: Solve for \(x\)

Simplify the equation: \(x+120^\circ = 180^\circ\). Subtract \(120^\circ\) from both sides: \(x=180^\circ - 120^\circ=60^\circ\).

Answer:

\(x = 60^\circ\)