Question

find the value of x. the diagram is not to scale. 73° 122° x° 180 - 122 = 58 73 + x + 58 = x = 180° - 131 x = 49

Explanation:

Step1: Find the adjacent interior angle

The angle adjacent to \(122^\circ\) on the straight line is supplementary to it. So, \(180 - 122 = 58^\circ\).

Step2: Use triangle angle - sum property

The sum of the interior angles of a triangle is \(180^\circ\). Let the three angles of the triangle be \(73^\circ\), \(58^\circ\), and \(x^\circ\). Then \(73 + 58 + x=180\).
First, calculate \(73 + 58 = 131\). Then, \(x = 180 - 131\).

Step3: Calculate the value of \(x\)

\(x=49\).

Answer:

\(x = 49\)