Question

1. find each angle. value of x____

∠d =____
∠f =____
exterior angle=____

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
So, \((x + 8)+3x=5x - 13\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+3x + 8=5x - 13\), which gives \(4x+8 = 5x - 13\)

Step3: Solve for \(x\)

Subtract \(4x\) from both sides: \(4x - 4x+8=5x-4x - 13\), so \(8=x - 13\)
Add \(13\) to both sides: \(x=8 + 13=21\)

Step4: Find \(\angle D\)

Substitute \(x = 21\) into \(\angle D=(x + 8)^{\circ}\). Then \(\angle D=(21 + 8)^{\circ}=29^{\circ}\)

Step5: Find \(\angle F\)

Substitute \(x = 21\) into \(\angle F = 3x^{\circ}\). Then \(\angle F=3\times21^{\circ}=63^{\circ}\)

Step6: Find the exterior angle

Substitute \(x = 21\) into \((5x - 13)^{\circ}\). Then \((5\times21-13)^{\circ}=(105 - 13)^{\circ}=92^{\circ}\)

Answer:

Value of \(x = 21\)
\(\angle D=29^{\circ}\)
\(\angle F = 63^{\circ}\)
Exterior angle \(=92^{\circ}\)