it is desired to draw a triangle so that the first angle

Question

is 5/4 of the second but is greater than one-half the third by 40 degree. what should be the magnitudes of the angles of the triangle?

Answer 1

Let the first angle be x, the second angle be y and the third angle be z.

the first angle is 5/4 of the second angle

So x is 5/4 of y (is means =, of means *)

x = 5/4*y (eq 1)

the first angle is greater than 1/2 the third angle by 40°

So, x is greater than 1/2 of z by 40

x = 1/2*z + 40 (eq 2)

We also know that all the angles in a triangle should be 180°

Therefore,

x + y + z = 180 (eq 3)

Then we can solve equation 2 for z and get

(x - 40) = 1/2*z

2(x - 40) = z (eq 4)

plug this in for z in eq 3

x + y + 2(x - 40) = 180

If we plug equation 1 into equation 3

5/4 * y + y + 2( 5/4 * y - 40) = 180

Then, we can solve for y

5/4 * y + y + 5/2 * y - 80 = 180

19/4 * y - 80 =180

19/4 * y = 260

y = 1040/19

Plug this value in for eq 1

x = (5/4)*y

x = (5/4) * (1040/19)

x = 1300/19

Plug this value in for eq 4

2(x - 40) = z

2(1300/19 - 40) = z

2(1300/19 - 760/19) = z

2(540 /19) = z

1080/19 = z

These are the magnitudes of the angles:

x = 1300/19

y = 1040/19

z = 1080/19