Answer:
x = 30 degrees
y = 67 degrees
z = 83 degrees
Explanation:
Since x, y , and z are the angle measure for the first, second and third angle respectively, we can write the following equations following the statements given:
The sum of the measures of the angles of a triangle is 180:
(1) x + y + z = 180
The sum of the measure of the second and third angle is five times the measure of the first angle:
(2) y + z = 5 x
The third angle is 16 more than the second:
(3) z = y + 16
Now we solve the system of three equations. We use the third equation to replace z in the second one:
y + (y + 16) = 5 x
then : 2 y = 5 x - 16; then y = 2.5 x - 8
So , now we can replace this expression for y in the third equation:
z = (2.5 x - 8) +16 = 2.5 x + 8
and finally we made the replacements of y and z shown above in bold, in the first equation:
x + (2.5 x - 8) + (2.5 x + 8) = 180
x + 5 x = 180
6 x = 180
then x = 180/6 = 30 degrees
From this, we get the value of the other angles:
y = 2.5 (30) - 8 = 67 degrees
z = 2.5 (30) +8 = 83 degrees