Question

1. what is the value of x? a) 71° b) 109° c) 116° d) 135°

Explanation:

Step1: Find the interior angle adjacent to \(x\)

Use the triangle angle - sum property. The sum of interior angles of a triangle is \(180^{\circ}\). Let the interior angle adjacent to \(x\) be \(y\). Then \(y=180-(45 + 64)\).

$$y=180 - 109=71^{\circ}$$

Step2: Calculate \(x\)

Since \(x\) and \(y\) are supplementary angles (\(x + y=180^{\circ}\)), then \(x = 180 - y\). Substitute \(y = 71^{\circ}\) into the formula.

$$x=180-71 = 109^{\circ}$$

Answer:

\(109^{\circ}\) (Option b)