Question

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles 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, respectively. Find the measures of the three angles

Answer 1

x=30 y=67 z=83

Explanation:

The solution is therefore (30,67,83).

Answer 2

First: 30°

Second: 67°

Third: 83°

Explanation:

First: x

Second: y

Third: z = y + 16

Constraints:

x + y + z = 180

y + z = 5x ===> y = 5x - z

Substitution to find first angle x:

x + y + z = 180

x + (5x - z) + z = 180

x + 5x - z + z = 180

6x = 180

x = 30

Substitution to find second angle y:

y = 5x - z

y = 5(30) - z

y = 150 - z

y = 150 - (y + 16)

y = 150 - y - 16

y = 134 - y

2y = 134

y = 67

Substitution to find third angle z:

z = y + 16

z = (67) + 16

z = 83