Question

for items 7 - 9, use the figure shown. what is the value of x? a 28 b 44 c 136 d 224

Explanation:

Step1: Recall triangle - angle - sum property

The sum of the interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(z\). So, \(z=180-(82 + 54)\).
\[z=180-(82 + 54)=180 - 136=44^{\circ}\]

Step2: Use the property of a linear pair

The angle \(x\) and the third - interior angle \(z\) of the triangle form a linear pair. A linear pair of angles is supplementary, meaning \(x + z=180^{\circ}\). Since \(z = 44^{\circ}\), then \(x=180 - z\).
\[x=180 - 44=136^{\circ}\]

Answer:

C. 136