# In the tri angles of a triangle angle B exceeds twice angle A by 15. Express the measure of angle C in terms of angle A.

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The interior angle sum of a triangle is equal to 180 degrees. Therefore, A + B + C = 180.

When we translate the statement from words into an equation we have: B = 2A + 15.

We can substitute (2A + 15) for B into the equation to get:

A + (2A + 15) + C = 180.

To solve for the equation in terms of C we need to simplify, and then "move" everything to the right side of the equation as shown below:

A + (2A + 15) + C = 180

3A + 15 + C = 180 Combine like terms

- 15 - 15 Subtract 15 from both sides

3A + C = 165

-3A -3A Subtract 3A from both sides

C = 165 - 3A

To double-check for correctness you may substitute the new value for C into the equation:

A + (2A + 15) + (165 - 3A) = 180

180 = 180

The sum of the angles of the triangle ABC is 180 degrees:

A + B + C =180 (1)

The measure of the angle B is:

B = 2A + 15 (2)

We'll substitute (2) in (1):

A + 2A + 15 + C = 180

We'll combine like terms:

3A + C + 15 = 180

We'll subtract 15 both sides:

3A + C = 180 - 15

3A + C = 165

We'll subtract 3A both sides:

C = 165 - 3A

**The measure of the angle C, in terms of the angle A, is:**

**C = 165 - 3A degrees**

Since angle B exceed twice A by 15, we have B = 2A+15.

Therefore A+B+C = A+(2A+15)+C which should be 180 degrees, as the sum of the 3 angles of a triangle is 180 degree.

A+2A+15 +C = 180.

3A+15 +C = 180.

Subtract 3A+15 from both sides:

Therefore C = 180 - (3A+15)

C = 180-15 - 3A

C = 165-3A. Thus we expressed C in terms of A.

In a triangle the sum of the angles is 180 degrees.

Or A + B + C = 180.

Also, it is given that the angle B exceeds twice angle A by 15. Therefore we have B= 2*A + 15.

Hence we we can write A + B + C = 180 as

A + B + C = 180

=> A + 2*A + 15 + C = 180

=> 3*A + 15 + C = 180

=> C = 180- 15 - 3*A

=> C = 165 - 3*A

**Therefore we can write C in terms of A as 165 - 3*A**