Question

1. find each angle. value of x__ ∠h= ∠i= exterior angle=__

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \((3x + 2)=(2x + 2)+42\)

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find \(\angle H\)

Substitute \(x = 42\) into \(\angle H=(2x + 2)\)
\(\angle H=2\times42+2=84 + 2=86^{\circ}\)

Step4: Find \(\angle I\)

Substitute \(x = 42\) into \(\angle I=(x + 10)\)
\(\angle I=42+10=52^{\circ}\)

Step5: Find the exterior angle

Substitute \(x = 42\) into \((3x + 2)\)
The exterior angle \(=3\times42+2=126+2=128^{\circ}\)

Answer:

Value of \(x = 42\)
\(\angle H = 86^{\circ}\)
\(\angle I = 52^{\circ}\)
Exterior angle \(=128^{\circ}\)