Question

1. x=44° 14. x=88°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Solve for x in problem 13

For the first triangle with angles 66°, 30°, and x, we have the equation $x + 66^{\circ}+30^{\circ}=180^{\circ}$. Then $x=180^{\circ}-(66^{\circ} + 30^{\circ})=180^{\circ}-96^{\circ}=84^{\circ}$.

Step3: Recall exterior - angle property of a triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step4: Solve for x in problem 14

For the second triangle, the exterior angle x is equal to the sum of the two non - adjacent interior angles 40° and 48°. So $x = 40^{\circ}+48^{\circ}=88^{\circ}$.

Answer:

1. $x = 84^{\circ}$
2. $x = 88^{\circ}$