Question

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

Explanation:

Step1: Use triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). Let the third - angle of the triangle (not adjacent to \(x\)) be \(A\). Then \(A + 54^{\circ}+82^{\circ}=180^{\circ}\). So, \(A=180^{\circ}-(54^{\circ} + 82^{\circ})\).

$$A = 180^{\circ}-136^{\circ}=44^{\circ}$$

Step2: Use linear - pair or adjacent - angle property

\(x\) and \(A\) are adjacent angles forming a linear pair (sum of adjacent angles on a straight line is \(180^{\circ}\)). But also, we can use the exterior - angle property. The exterior - angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, \(x\) is an interior angle (not an exterior angle in the wrong sense). Wait, no, actually, if we consider the straight - line, we made a mistake above. The correct approach is:
The sum of angles in a triangle is \(180^{\circ}\). Let's re - do it.
The sum of the three interior angles of a triangle is \(180^{\circ}\). If we consider the triangle with angles \(54^{\circ}\), \(82^{\circ}\), and the angle adjacent to \(x\). Let the angle adjacent to \(x\) be \(a\). Then \(a+54^{\circ}+82^{\circ}=180^{\circ}\), so \(a = 180-(54 + 82)=44^{\circ}\). And since \(x\) and \(a\) are adjacent angles on a straight line (\(x + a=180^{\circ}\)), no, wait, no! Wait, the problem is to find \(x\). The sum of the interior angles of a triangle: \(x+54^{\circ}+82^{\circ}=180^{\circ}\) (because the three angles of the triangle are \(54^{\circ}\), \(82^{\circ}\), and \(x\)).

$$x=180-(54 + 82)$$

$$x = 180 - 136$$

$$x=44^{\circ}$$

Answer:

\(44\)