Question

The lengths of two sides of a triangle are 10 inches and 4 inches. Which of the following dimensions is the third side of this triangle?

4 inches
5 inches
6 inches
7 inches

The angles shown below are supplementary:

A pair of supplementary angles is shown. One angle measures 10x and the other angle measures 70 degrees.

What is the value of x?

10°
11°
20°
21°

Answer 1

First part:

The triangle would look like a triangle only if the third side is 7 inches.

The third side could be 6 inches, but then all 3 sides would lie on a straight
line, and you couldn't tell that it's a triangle.

The third side can't be 4 inches or 5 inches, because it would be too short
to join the ends of the first 2 sides.


Second part:

If the angles are supplementary, that means that
they add up to 180° .

Let's addum up:
10x + 70° = 180°

Subtract 70° from each side: 10x = 110°

Divide each side by 10: x = 11°