Question

b.

x = ____

Explanation:

Step1: Find the interior - angle adjacent to 134°.

The sum of an interior - angle and its adjacent exterior - angle of a triangle is 180°. Let the interior - angle adjacent to 134° be \(y\). Then \(y + 134^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-134^{\circ}=46^{\circ}\).

Step2: Use the angle - sum property of a triangle.

The sum of the interior angles of a triangle is 180°. In the triangle, we know one angle is 49° and another is \(y = 46^{\circ}\), and let the third angle be \(z\). Then \(49^{\circ}+46^{\circ}+z = 180^{\circ}\), so \(z=180^{\circ}-(49^{\circ}+46^{\circ}) = 85^{\circ}\).

Step3: Find the value of \(x\).

The angle \(x\) and \(z\) are supplementary (a straight - line is 180°). So \(x+z = 180^{\circ}\). Since \(z = 85^{\circ}\), then \(x=180^{\circ}-85^{\circ}=95^{\circ}\).

Answer:

\(95^{\circ}\)