Question

The second angle of a triangle is 68 more than the first angle. The third angle is two times the first. Find the three angles.

First angle: _____

Second angle: _____

Third angle ______

Answer 1

To find the angles of the triangle, algebraic equations were created using the given relationships and the fact that a triangle's angles sum to 180 degrees. The first angle is found to be 28 degrees, from which the second and third angles are determined to be 96 degrees and 56 degrees, respectively.

Step-by-step explanation:

To find the three angles of a triangle given that the second angle is 68 degrees more than the first angle, and the third angle is two times the first angle, we will use the fact that the sum of the angles in a triangle is always 180 degrees. Let's define the first angle as x degrees.

According to the problem:

• The second angle would be x + 68 degrees.
• The third angle would be 2x degrees.

By summing up all the angles and setting their sum equal to 180 degrees, we get the equation:

x + (x + 68) + 2x = 180

Combining like terms, we get:

4x + 68 = 180

Subtracting 68 from both sides gives us:

4x = 112

Dividing both sides by 4, we find that:

x = 28 degrees

Therefore, the first angle is 28 degrees.

Using x to find the other angles:

• The second angle is x + 68 = 28 + 68 = 96 degrees.
• The third angle is 2x = 2(28) = 56 degrees.

Answer 2

let the first angle be a

then

second angle= 68+a

third angle=2a

we know

a+b+c=180 [sum of interior angle of triangle is 180]

a+68+a+2a=180

4a=180-68

a=28

Hence

first angle=28

second angle = 96

third angle =56