Question

find the values of x and y.
(12x - 4)°
(4y)°
(5y)°
x =
y =

Explanation:

Step1: Use angle - sum property at point R

The sum of angles around a point is 360°. At point R, we have a right - angle (90°) and the other angles are (12x - 4)°, (4y)°, and (5y)°. So, (12x - 4)+4y + 5y+90 = 360.

Step2: Simplify the equation for y

First, combine like terms for the y - terms: (12x - 4)+9y+90 = 360. Then, 12x+9y + 86 = 360. But we can also note that the non - right angles (4y)° and (5y)° are complementary to the angle (12x - 4)° with respect to the 360° around the point. Another way is to consider the fact that 4y+5y = 90 (since the right - angle is 90° and these two angles are part of a linear - pair with the non - right part of the 360° around the point). So, 9y=90.
Solve for y:
\[y=\frac{90}{9}=10\]

Step3: Substitute y into the equation to find x

Substitute y = 10 into the equation 12x-4+4y + 5y+90 = 360.
12x-4+4(10)+5(10)+90 = 360.
12x-4 + 40+50+90 = 360.
12x-4+180 = 360.
12x+176 = 360.
12x=360 - 176.
12x = 184.
\[x=\frac{184}{12}=\frac{46}{3}\]

Answer:

\[x=\frac{46}{3},y = 10\]