Q:

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

Accepted Solution

A:
Answer: The value of x = 0.5, y = 0.8 and z = 0.9Step-by-step explanation:From the given figure. Let's form the equations50z + 13 + 45x + [tex]\frac{19}{2}[/tex] = 90°45x + 50z + 13 + 9.5 = 9045x + 50z + 22.5 = 9045x + 50z = 90 - 22.545x + 50z = 67.5  --------------------------(1)[tex]\frac{225y}{2} = 90[/tex]° Because it is a right angle.225y = 180y = [tex]\frac{180}{225}[/tex]y = 0.8   --------------------(2)44x + 125y + 80z -14 = 180° because they are supplementary angles add upto 180 degrees.44x + 125y + 80z = 180 + 1444x +125y + 80z = 194  ------------(3)Now plug in y = 0.8 in the above equation (3), we get44x + 125 times 0.8 + 80z = 19444x + 100 + 80z = 19444x + 80z = 194 - 10044x + 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 z44(0.5) + 80z = 9422 + 80z = 9480z = 94 - 2280z = 72z = [tex]\frac{72}{80}[/tex]z = 0.9Therefore, the value of x = 0.5, y = 0.8 and z = 0.9