Question

Which set of three angles could represent the interior angles of a triangle?
19 degrees, 70 degrees, 91 degrees
47 degrees, 12 degrees, 31 degrees
50 degrees, 20 degrees, 20 degrees
25 degrees, 25 degrees, 100 degrees

Answer 1

Answer:

19° ,70° and 91° only one represent the interior angle of triangle.

because the sum of these angle is 180°

other set doesn't represent angle of triangle

hope it helps

thanks for giving me a chance to help you

Answer 2

Given : The given sets of three angles are :

1. 19°,70°,91°
2. 19°,70°,91°47°,12°,31°
3. 19°,70°,91°47°,12°,31°50°,20°,20°
4. 19°,70°,91°47°,12°,31°50°,20°,20°25°,25°,100°

To find : The set of the three angles which can represent the interior angles of a triangle.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to determine the required set of three angles)

Now, we know that :

Sum of three interior angles of a triangle is always equal to 180°.

So, the set of three angles which has a sum of 180° will be set of three angles which can represent the three interior angles of a triangle.

The sums are :

• 19° + 70° + 91° = 180°
• 47° + 12° + 31° = 90°
• 50° + 20° + 20° = 90°
• 25° + 25° + 100° = 150°

So, only the first set of three angles (i.e. 19°,70°,91°) is able to produce 180° as the sum. That's why, only this set of three angles is able to represent the three interior angles of a triangle.

Hence, 19°,70°,91° could represent the interior angles of a triangle.