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PLEASE HELP BUT DON'T ANSWER UNLESS YOU ACTUALLY CAN HELP! 15 PTS!

A triangle has three angles. The second angle is 20 degrees more than the first. The third angle is 8 degrees more than the second. Find all three angles. Show your work please.

Respuesta :

altavistard

The key to solving this problem lies in representing the unknowns properly.

Let the first angle be a.  Then the second angle, b, is a+20.  The third angle is (a+20)+8.  Now all of the measurements of angle are in terms of a.  Fact:  the sum of all the angles of a triangle is 180 degrees.

Thus, a          +        a+20      + a+20+8  = 180, or:

3a + 48 = 180.

Solve for a by subtracting 48 from both sides:   3a = 132, or a = 44.

The first angle is a = 44 degrees.

The second angle is a+20 degrees, or 64 degrees.

The third angle is  a+20+8 degrees, or 72 degrees.

We must check to ensure that these 3 angles do add up to 180 degrees:

44+64+72 = 180

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