Question

find the values of x and y.
(7y - 4)°
(3y - 5)°
(12x + 3)°
59°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(7y - 4=12x + 3+59\). Also, \(3y - 5+12x + 3 = 180\) (linear - pair of angles). First, simplify \(7y - 4=12x + 62\), which gives \(7y-12x=66\). From \(3y - 5+12x + 3 = 180\), we get \(3y+12x=182\).

Step2: Add the two equations

Add \(7y-12x = 66\) and \(3y + 12x=182\). \((7y-12x)+(3y + 12x)=66 + 182\). This simplifies to \(10y=248\), so \(y=\frac{248}{10}=24.8\).

Step3: Substitute \(y\) value into an equation

Substitute \(y = 24.8\) into \(3y+12x=182\). \(3\times24.8+12x=182\). \(74.4+12x=182\). Then \(12x=182 - 74.4=107.6\). So, \(x=\frac{107.6}{12}=\frac{1076}{120}=\frac{269}{30}\approx8.97\).

Answer:

\(x=\frac{269}{30}\), \(y = 24.8\)