The sum of the measures of the angles of a triangle is 180. The sum of the measure of the second and third angle is five times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and ,z represent the measures of the first second and third angles

x = 30 degrees

y = 67 degrees

z = 83 degrees

Step-by-step 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

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step-by-step explanation: