Question

The angle measures are represented by algebraic expressions. determine the values of x y and z

Answer 1

The value of x = 0.5, y = 0.8 and z = 0.9

Explanation:

From the given figure. Let's form the equations

50z + 13 + 45x +
`(19)/(2)` = 90°

45x + 50z + 13 + 9.5 = 90

45x + 50z + 22.5 = 90

45x + 50z = 90 - 22.5

45x + 50z = 67.5 --------------------------(1)

`(225y)/(2) = 90`° Because it is a right angle.

225y = 180

y =
`(180)/(225)`

y = 0.8 --------------------(2)

44x + 125y + 80z -14 = 180° because they are supplementary angles add upto 180 degrees.

44x + 125y + 80z = 180 + 14

44x +125y + 80z = 194 ------------(3)

Now plug in y = 0.8 in the above equation (3), we get

44x + 125 times 0.8 + 80z = 194

44x + 100 + 80z = 194

44x + 80z = 194 - 100

44x + 80z = 94 ---------------------(4)

Now let's solve the equation (1) and (4) using elimination method.

x = 0.5

Now plug in x = 0.5 in the equation (4) and find the value of z

44(0.5) + 80z = 94

22 + 80z = 94

80z = 94 - 22

80z = 72

z =
`(72)/(80)`

z = 0.9

Therefore, the value of x = 0.5, y = 0.8 and z = 0.9