Question

3
15
24°
(3x + 6)°
(2x + 18)°
x=
exterior ∠=
remote interior ∠s=
____ and ____

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \((3x + 6)=(2x + 18)+24\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find the measure of the exterior angle

Substitute \(x = 36\) into \(3x+6\). So, \(3\times36+6=108 + 6=114\).

Step4: Identify the remote interior angles

The remote interior angles are \(24^{\circ}\) and \(2x+18\). Substitute \(x = 36\) into \(2x + 18\), \(2\times36+18=72+18 = 90\).

Answer:

\(x = 36\), Exterior \(\angle=114^{\circ}\), Remote interior \(\angle s=24^{\circ}\) and \(90^{\circ}\)