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

Answer: 30°, 67° e 83°.

Step-by-step explanation: The angles are (2x + 16)/5 , x e x + 16°

Adding all the angles, comes:

(2x + 16)/5 + x + x + 16° = 180° ;

2x + 16° + 5x + 5x + 80° = 900° ;

12x = 900° - 16° - 80° ;

12x = 804°° ;

x = 804°/12 ;

x = 67°

So, the first angle is (2,67 + 16)/5 = 30°, the second is 67° and the third is 83°.

Answer 2

Answer:

The measure of the three angles are; 30° , 67°  and 83°

Step-by-step explanation:

To solve this correctly, we need to be able to interpret the question statement correctly;

From the question, x, y and z represent the measures of the first, second and third angle respectively

that is x = first angle       y = second angle    and    z=third angle

Also from the question, the first statement is, the sum of the measure of the three angles is 180.

The mathematical interpretation of this statement is that;

x + y + z = 180  ------------(1)

Next statement is that; the sum of the measures of the second and third angles is five times the measure of the first angle

Its mathematical representation is;   y + z = 5x -----------(2)

The next statement is that; the third angle is 16 more than the second

its mathematical interpretation is; z = 16 + y   -------(3)

Haven gotten our 3 equations, we can now  proceed to solve for x, y and z.

substitute equation (2) in equation (1)

That is; substitute y + z = 5x in equation (1)

x + y + z = 180

x +   5x  = 180

6x   = 180

Divide both-side of the equation by 6

6x / 6   = 180/6

x = 30

Next is, to substitute equation (3) in equation (2)

That is; substitute z = 16 + y in equation (2)

 y + z = 5x

y  + 16+y = 5x

2y  + 16  = 5x

We can now substitute our x = 30 in the above equation

2y  + 16  = 5x

2y + 16 = 5(30)

2y + 16 = 150

subtract 16 from both-side of the equation

2y + 16 - 16 = 150 - 16

2y   = 134

Divide both-side of the equation by 2

2y/2 = 134/2

y = 67

To get the value of z, we can simply substitute y =67 into equation (3)

z = 16 + y

z = 16 + 67

z = 83

x = 30    y=67  and   z = 83

We can check our answer to see if we are correct;

x + y + z = 180

30 + 67 + 83 = 180

so our answer is correct.

Therefore, the measure of the three angles are 30°, 67° and 83°