The first angle of a triangle is 16 degrees less than the second angle.The third angle of the triangle is double the second angle. Find the angles of the triangle.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The angles of a triangle always equal 180 degrees. We need to express all our angles so that we can find the first and then calculate the others. This question then becomes one of problem-solving.

Let B= 2nd angle

`therefore A= B-16`   because it is 16 degrees less that the second angle.

`therefore...

See
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Get 48 Hours Free Access

The angles of a triangle always equal 180 degrees. We need to express all our angles so that we can find the first and then calculate the others. This question then becomes one of problem-solving.

Let B= 2nd angle

`therefore A= B-16`   because it is 16 degrees less that the second angle.

`therefore C = 2B` because it is twice(double) the second angle

Now we can express all our angles in terms of <B

As they are equal to 180 degrees (properties of a triangle) and

A + B + C = 180

substitute the equivalent values in terms of the problem to be solved:

`therefore (B-16)+ B + 2B=180 `

`therefore`  4B -16 = 180

`therefore 4B=180+16`

`therefore 4B=196`

`therefore B=196/4`

`therefore` B= 49 degrees

`therefore ` A= B-16= 49-16= 33

and C= 2B= 2(49)= 98

A: 33 degrees; B: 49 degrees; C:98 degrees

 

 

Approved by eNotes Editorial Team