Question

c.
m j
k
(2x + 4)°
132°
l
112°
n
x =

Explanation:

1. Recall the exterior - angle property of a triangle:

• The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles.
• In \(\triangle KJL\), the exterior angle at \(J\) is \(132^{\circ}\), and the exterior angle at \(L\) is \(112^{\circ}\).
• The non - adjacent interior angles to the exterior angle at \(J\) are \(\angle K\) and the non - adjacent interior angle to the exterior angle at \(L\) is also related to the angles of the triangle.
• First, find the interior angle at \(J\): The interior angle at \(J\) is \(180 - 132=48^{\circ}\) (since an exterior angle and its adjacent interior angle are supplementary).
• The interior angle at \(L\) is \(180 - 112 = 68^{\circ}\) (because an exterior angle and its adjacent interior angle are supplementary).
• In \(\triangle KJL\), we know that the sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle K+(180 - 132)+(180 - 112)=180\).
• Substitute the values: \((2x + 4)+48+68 = 180\).
• Combine like terms: \(2x+4 + 116=180\).
• Then \(2x+120 = 180\).
• Subtract 120 from both sides: \(2x=180 - 120\).
• So, \(2x = 60\).
• Divide both sides by 2: \(x = 30\).

Answer:

30