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°
