Question

Exterior angle, theorem, and triangle sum theorem

Answer 1

x = 4

The two interior angles are

14x + 6 = 14 x 4 + 6 = 62°

16x + 4 = 16 x 4 + 4 = 68°

Explanation:

The exterior angle of a triangle is the sum of the interior angles:

Here the exterior angle is 130° and the interior angles are
16x + 4 and 14x + 6

So 16x + 4 + 14x + 6 = 130

Gathering like terms and simplifying:
16x + 14x + 4 + 6 = 130

30x + 10 = 130

30x = 120 (subtract 10 from both sides)

x = 4

The two interior angles are

14x + 6 = 14 x 4 + 6 = 62°

16x + 4 = 16 x 4 + 4 = 68°