Question

For each set of angles, decide if there is a triangle whose angles have these measures in degrees: 1. 60, 60, 60 2. 90, 90, 45 3. 30, 40, 50 4.90, 45, 45 5. 120, 30, 30 If you get stuck, consider making a line segment. Then use a protractor to measure angles with the first two angle measures.

Answer 1

The sum of the internal angles of a triangle must be equal to 180 degrees. We can add the three angles in each case to check wheter there is a triangle with those measurements.

1. 60,60,60

`60+60+60=180`

The sum of these three angles adds to 180 degrees, therefore there is a triangle with these measurements.

2. 90,90,45

The sum of these three angles adds to 225 degrees, therefore there isn't a triangle with these measurements

`90+90+45=225`

3. 30,40,50

The sum of these three angles adds up to 120 degrees, therefore there isn't a triangle with these measurements.

`30+40+50=120`

4. 90,45,45

The sum of these three angles adds up to 180 degrees, therefore there is a triangle with these measurements.

`90+45+45=180`

5. 120,30,30

The sum of these three angles adds up to 180 degrees, therefore there is a triangle with these measurements.

`120+30+30=180`

The ones that form triangles are 1, 4 and 5.