Question

Solve. Check to see if your answer is reasonable.

Parking Lot A triangular region of the community college parking lot was measured. The measure of the first angle of this triangle is double the measure of the second angle. The measure of the third angle is 19° greater than double the measure of the first angle. What are the measurements of all three angles?

Answer 1

Let the first angle be x, the second angle be y, and the third angle be z.

The measure of the first angle is double the measure of the second angle. This would be represented by

The measure of the third angle is 19 degrees greater than double the measure of the first angle. This would be represented by

The sum of all three angles must be 180 therefore. By direct substitution this would be.

Substitute one more time to eliminate the x and get all the variables to be y. This would be:

Find the missing measure using order of operations to get:

Substitute this value back into the first equation to get:

Substitute this value back into the third equation to get:

Therefore, the angles are