x, y - the angles
The measures of the angles in a linear pair add up to 180°.
\(x+y=180 \\
y=180-x\)
The ratio of x to y is 6:4.
\(\frac{x}{y}=\frac{6}{4} \\ \\
\frac{x}{180-x}=\frac{6}{4} \\
4x=6(180-x) \\
4x=1080-6x \\
4x+6x=1080 \\
10x=1080 \\
x=108 \\ \\
y=180-x=180-108=72\)
The measures of the angles are: 108° and 72°.
