Question

On a piece of paper, draw a triangle so that one of the angle measures 80° and another angle measures 40°.

Measure the third angle and measure the side lengths.

Select two true statements.

Question 1 options:

The measure of the third angle is 20°.

The measure of the third angle is 40°.


The measure of the third angle is 60°.


All the side lengths are different.

Answer 1

To find the missing angle in a triangle when two angles are known, we can use the fact that the sum of the angles in a triangle is always 180°. You are given one angle measuring 80° and another measuring 40°.

Let's calculate the third angle:

\[
\text{Third angle} = 180° - (80° + 40°)
\]
\[
\text{Third angle} = 180° - 120° = 60°
\]

So the measure of the third angle is 60°.

Now, let's evaluate the statements:

1. **The measure of the third angle is 20°.** (False)
2. **The measure of the third angle is 40°.** (False)
3. **The measure of the third angle is 60°.** (True)
4. **All the side lengths are different.** (True, because the angles 80°, 40°, and 60° are all different, which means the triangle is scalene with all sides of different lengths.)

Thus, the two true statements are:

- The measure of the third angle is 60°.
- All the side lengths are different.