Question

a side of the triangle below has been extended to form an exterior angle of 153°. find the value of x.

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). The exterior angle \(153^\circ\) and the adjacent interior angle of the triangle form a linear pair. Let the adjacent interior angle be \(y\). So, \(153^\circ + y = 180^\circ\). Solving for \(y\), we get \(y = 180^\circ - 153^\circ = 27^\circ\).

Step2: Use triangle angle sum property

The triangle is a right triangle (one angle is \(90^\circ\)), so the sum of its interior angles is \(180^\circ\). Let the angles be \(x\), \(y = 27^\circ\), and \(90^\circ\). Then \(x + 27^\circ + 90^\circ = 180^\circ\). Simplifying, \(x + 117^\circ = 180^\circ\). Solving for \(x\), we get \(x = 180^\circ - 117^\circ = 63^\circ\).

Answer:

\(x = 63\)