Question

ch angle.
8)
(5x + 62)°
37°
(3x + 47)°

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, \(3x + 47=(5x + 62)+37\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Subtract \(3x\) from both sides: \(47 = 2x+99\). Then subtract \(99\) from both sides: \(2x=47 - 99=-52\). Divide by \(2\): \(x=-26\).

Step4: Calculate the angles

For \((5x + 62)^{\circ}\): Substitute \(x =-26\), \(5\times(-26)+62=-130 + 62=-68\) (This is wrong, we made a mistake above. Let's correct the equation. The correct exterior - angle formula: \((3x + 47)=(5x+62)-37\))

$$
LATEXBLOCK1
$$

For \((5x + 62)^{\circ}\): \(5\times11+62=55 + 62 = 117^{\circ}\)
For \((3x + 47)^{\circ}\): \(3\times11+47=33 + 47=80^{\circ}\)

Answer:

The angles are \(37^{\circ}\), \(117^{\circ}\), and \(80^{\circ}\)