Question

1. find x.
2. find the measure of <1.

Explanation:

Step1: Recognize the triangle type

The triangle in problem 3 is equilateral (all sides are equal, so all angles are equal). Each angle of an equilateral triangle is \(60^{\circ}\). So, \(9x - 3=60\).

Step2: Solve for \(x\)

Add \(3\) to both sides: \(9x=60 + 3=63\).
Divide both sides by \(9\): \(x=\frac{63}{9}=7\).

For problem 4:

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. Let the exterior angle be \(126^{\circ}\), and the non - adjacent interior angles be \(\angle1\) and \(48^{\circ}\). So, \(\angle1+48^{\circ}=126^{\circ}\).

Step2: Solve for \(\angle1\)

Subtract \(48^{\circ}\) from both sides: \(\angle1=126^{\circ}-48^{\circ}=78^{\circ}\).

Answer:

For problem 3: \(x = 7\)
For problem 4: \(\angle1=78^{\circ}\)