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

1st part is 64,000,000

2nd part 500,000

step-by-step explanation:

area of rectangle a is 2 times that of rectangle b that means 2x+x =   36cm^2

3x = 36cm ^2

x = 36/3

x= 12cm^2

and 2x = 24cm^2

now side of square = are divided by sides = 36/4 = 6cm

that means length of rectangle a and b is 6cm too

now for rectangle a,

l*b = area

= 6*y=24

y=24/6 = 4

therefore dimensions of rectangle a are- length = 6cm, breadth = 4cm

and for rectangle b, length = 6cm and breadth = 6-4 = 2cm.

hope this .